Multiple Stable Solutions of Nonlinear Boundary Value Problems Arising in Chemical Reactor Theory
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
R. Aris, On stability criteria of chemical reaction engineering, Chem. Engrg. Sci., 24 (1968), 149–169
2.
D. Luss, Sufficient conditions for uniqueness of the steady state solutions in distributed parameter systems, Chem. Engrg. Sci., 23 (1968), 1249–1255
3.
Julian D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1968vi+260
4.
Murray H. Protter, Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall Inc., Englewood Cliffs, N.J., 1967x+261
5.
Donald S. Cohen, Theodore W. Laetsch, Nonlinear boundary value problems suggested by chemical reactor theory., J. Differential Equations, 7 (1970), 217–226
6.
R. Bruce Simpson, Donald S. Cohen, Positive solutions of nonlinear elliptic eigenvalue problems, J. Math. Mech., 19 (1969/70), 895–910
7.
Herbert B. Keller, Donald S. Cohen, Some positone problems suggested by nonlinear heat generation, J. Math. Mech., 16 (1967), 1361–1376
8.
Herbert B. Keller, Elliptic boundary value problems suggested by nonlinear diffusion processes, Arch. Rational Mech. Anal., 35 (1969), 363–381
9.
Herbert B. Keller, Positive solutions of some nonlinear eigenvalue problems, J. Math. Mech., 19 (1969/1970), 279–295
10.
L. R. Raymond, N. R. Amundson, Some observations on tubular reactor stability, Canad. J. Chem. Engrg., 42 (1964), 173–177
11.
N. R. Amundson, Some further observations on tubular reactor stability, Canad. J. Chem. Engrg., 43 (1965), 49–55
12.
N. R. Amundson, D. Luss, Qualitative and quantitative observations on the tubular reactor, Canad. J. Chem. Engrg., 46 (1968), 424–433
Information & Authors
Information
Published In
Copyright
Copyright © 1971 Society for Industrial and Applied Mathematics.
History
Submitted: 5 January 1970
Published online: 12 July 2006
Authors
Metrics & Citations
Metrics
Citations
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited By
- Existence of S-shaped type bifurcation curve with dual cusp catastrophe via variational methodsJournal of Differential Equations, Vol. 334 | 1 Oct 2022
- The Method of Upper and Lower Solutions to Impulsive Differential Equation with Sturm–Liouville Integral Boundary ConditionsDifferential Equations and Dynamical Systems, Vol. 30, No. 2 | 10 August 2018
- Some Sufficient Conditions for Compactness of Linear Hammerstein Integral Operators and ApplicationsIntegral Equations and Operator Theory, Vol. 94, No. 1 | 21 February 2022
- Green's functions, linear second‐order differential equations, and one‐dimensional diffusion advection modelsStudies in Applied Mathematics, Vol. 147, No. 1 | 17 April 2021
- Four computational approaches for solving a class of boundary value problems arising in chemical reactor industryApplied Mathematics and Computation, Vol. 355 | 1 Aug 2019
- Complex numerical-experimental investigations of combustion in model high-speed combustor ductsActa Astronautica, Vol. 158 | 1 May 2019
- Nonlinear Boundary Value Problems500 Examples and Problems of Applied Differential Equations | 24 September 2019
- Linearized domain decomposition approaches for nonlinear boundary value problemsJournal of Computational and Applied Mathematics, Vol. 346 | 1 Jan 2019
- Positive global solutions of nonlocal boundary value problems for the nonlinear convection reaction-diffusion equationsBoundary Value Problems, Vol. 2017, No. 1 | 10 January 2017
- Bifurcations and symmetry in two optimal formation control problems for mobile robotic systemsRobotica, Vol. 35, No. 8 | 14 July 2016
- New fixed point index results and nonlinear boundary value problemsBulletin of the London Mathematical Society, Vol. 49, No. 3 | 21 April 2017
- Shooting homotopy analysis methodEngineering Computations, Vol. 34, No. 2 | 18 Apr 2017
- Positive solutions of higher-order Sturm-Liouville boundary value problems with derivative-dependent nonlinear termsBoundary Value Problems, Vol. 2016, No. 1 | 10 June 2016
- Bifurcation curves in a combustion problem with general Arrhenius reaction-rate lawsANNALI DELL'UNIVERSITA' DI FERRARA, Vol. 62, No. 2 | 29 July 2016
- Multiple positive radial solutions to some Kirchhoff equationsJournal of Mathematical Analysis and Applications, Vol. 440, No. 1 | 1 Aug 2016
- Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear termsBoundary Value Problems, Vol. 2015, No. 1 | 30 January 2015
- Efficient Numerical Methods for Singularly Perturbed Differential EquationsMathematical Modeling with Multidisciplinary Applications | 2 August 2013
- Numerical solution of nonlinear singularly perturbed problems on nonuniform meshes by using a non-standard algorithmJournal of Mathematical Chemistry, Vol. 48, No. 1 | 12 November 2009
- Positive solutions for a higher-order four-point boundary value problem with a p -LaplacianComputers & Mathematics with Applications, Vol. 58, No. 6 | 1 Sep 2009
- Existence and uniqueness of positive solutions for an integral boundary value problemNonlinear Analysis: Theory, Methods & Applications, Vol. 69, No. 11 | 1 Dec 2008
- A survey on various computational techniques for nonlinear elliptic boundary value problemsAdvances in Engineering Software, Vol. 39, No. 9 | 1 Sep 2008
- Numerical Methods for Quasi‐Linear Elliptic Equations with Nonlinear Boundary ConditionsSIAM Journal on Numerical Analysis, Vol. 45, No. 3 | 7 May 2007
- Multiple fixed-sign solutions for a system of difference equations with Sturm–Liouville conditionsJournal of Computational and Applied Mathematics, Vol. 183, No. 1 | 1 Nov 2005
- Positive solutions of singular differential equations on measure chainsComputers & Mathematics with Applications, Vol. 49, No. 5-6 | 1 Apr 2005
- Three fixed-sign solutions of system model with Sturm–Liouville type conditionsJournal of Mathematical Analysis and Applications, Vol. 298, No. 1 | 1 Oct 2004
- On multiple fixed-sign solutions of a discrete system with Hermite boundary conditionsJournal of Mathematical Analysis and Applications, Vol. 297, No. 1 | 1 Sep 2004
- Accelerated monotone iterations for numerical solutions of nonlinear elliptic boundary value problemsComputers & Mathematics with Applications, Vol. 46, No. 10-11 | 1 Nov 2003
- Existence of multiple solutions for finite difference approximations to second-order boundary value problemsNonlinear Analysis: Theory, Methods & Applications, Vol. 53, No. 1 | 1 Apr 2003
- ReferencesModeling MEMS and NEMS | 3 December 2009
- On Eigenvalue Intervals and Eigenfunctions of Nonresonance Singular Dirichlet Boundary Value ProblemsActa Mathematicae Applicatae Sinica, English Series, Vol. 18, No. 4 | 1 Nov 2002
- Existence theorems for a system of difference equations with (n,p)-type conditionsApplied Mathematics and Computation, Vol. 123, No. 3 | 1 Oct 2001
- Further results on fixed-sign solutions for a system of higher-order difference equationsComputers & Mathematics with Applications, Vol. 42, No. 3-5 | 1 Aug 2001
- Eigenvalue problems for a conjugate difference equationApplicable Analysis, Vol. 76, No. 1-2 | 1 Oct 2000
- Generalized multipoint conjugate eigenvalue problemsMathematical and Computer Modelling, Vol. 32, No. 5-6 | 1 Sep 2000
- Triple positive solutions of conjugate boundary value problems IIComputers & Mathematics with Applications, Vol. 40, No. 4-5 | 1 Aug 2000
- Criteria for multiple solutions of difference and partial difference equations subject to multipoint conjugate conditionsNonlinear Analysis: Theory, Methods & Applications, Vol. 40, No. 1-8 | 1 Apr 2000
- A System of (ni,pi) Boundary Value Problems with Positive/Nonpositive NonlinearitiesJournal of Mathematical Analysis and Applications, Vol. 243, No. 2 | 1 Mar 2000
- Positive Solutions of Semilinear Elliptic Boundary Value Problems in Chemical Reactor TheoryDirect and Inverse Problems of Mathematical Physics | 1 Jan 2000
- Eigenvalue theorems for discrete multipoint conjugate boundary value problemsJournal of Computational and Applied Mathematics, Vol. 113, No. 1-2 | 1 Jan 2000
- Eigenvalues and eigenfunctions of discrete conjugate boundary value problemsComputers & Mathematics with Applications, Vol. 38, No. 3-4 | 1 Aug 1999
- Positive solutions and eigenvalues of conjugate boundary value problemsProceedings of the Edinburgh Mathematical Society, Vol. 42, No. 2 | 20 January 2009
- A “Booster method” for singular perturbation problems arising in chemical reactor theoryApplied Mathematics and Computation, Vol. 100, No. 1 | 1 Apr 1999
- An application of topological transversality to non-positive higher order difference equationsApplied Mathematics and Computation, Vol. 99, No. 2-3 | 1 Mar 1999
- Existence of multiple positive solutions of discrete two-pointJournal of Difference Equations and Applications, Vol. 5, No. 6 | 1 Jan 1999
- Positive Solutions of Difference Equations with Two-Point Right Focal Boundary ConditionsJournal of Mathematical Analysis and Applications, Vol. 224, No. 1 | 1 Aug 1998
- Multiple positive solutions of two-point right focal boundary value problemsMathematical and Computer Modelling, Vol. 28, No. 3 | 1 Aug 1998
- On eigenvalue intervals and twin eigenfunctions of higher-order boundary value problemsJournal of Computational and Applied Mathematics, Vol. 88, No. 1 | 1 Feb 1998
- Existence of positive solutions for non-positive higher-order BVPsJournal of Computational and Applied Mathematics, Vol. 88, No. 1 | 1 Feb 1998
- Semilinear Elliptic Boundary Value Problems in Chemical Reactor TheoryJournal of Differential Equations, Vol. 142, No. 2 | 1 Jan 1998
- Eigenvalue characterization for (n · p) boundary-value problemsThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, Vol. 39, No. 3 | 17 February 2009
- ‘Shooting method' for singular perturbation problems arising in chemical reactor theoryInternational Journal of Computer Mathematics, Vol. 70, No. 2 | 19 March 2007
- Positive solutions of discrete (n,p) boundary value problemsNonlinear Analysis: Theory, Methods & Applications, Vol. 30, No. 1 | 1 Dec 1997
- Existence of positive solutions for nonpositive difference equationsMathematical and Computer Modelling, Vol. 26, No. 7 | 1 Oct 1997
- Existence and estimates of twin positive solution for two-point right focal boundary value problemsApplicable Analysis, Vol. 67, No. 1-2 | 2 May 2007
- Existence of positive solutions for higher order difference equationsApplied Mathematics Letters, Vol. 10, No. 5 | 1 Sep 1997
- Double positive solutions of (n,p) boundary value problems for higher order difference equationsComputers & Mathematics with Applications, Vol. 32, No. 8 | 1 Oct 1996
- Eigenvalues of generalized Gelfand modelsNonlinear Analysis: Theory, Methods & Applications, Vol. 20, No. 12 | 1 Jun 1993
- An example of nonlinear toxic mass spreadingApplied Scientific Research, Vol. 47, No. 4 | 1 Oct 1990
- Asymptotic behavior of solutions for finite-difference equations of reaction-diffusionJournal of Mathematical Analysis and Applications, Vol. 144, No. 1 | 1 Nov 1989
- REFERENCESNonlinear Problems in Abstract Cones | 1 Jan 1988
- Monotone iterative methods for finite difference system of reaction-diffusion equationsNumerische Mathematik, Vol. 46, No. 4 | 1 Dec 1985
- Multiple solutions of a boundary-value problem in enzyme kineticsAdvances in Applied Mathematics, Vol. 6, No. 2 | 1 Jun 1985
- Existence of coupled quasi-solutions of systems of nonlinear elliptic boundary value problemsNonlinear Analysis: Theory, Methods & Applications, Vol. 8, No. 5 | 1 May 1984
- Monotone methods for periodic solutions of second order scalar functional differential equationsNumerische Mathematik, Vol. 42, No. 1 | 1 Mar 1983
- Half-stable solution branches for ordinary bifurcation problemsMathematical Methods in the Applied Sciences, Vol. 5, No. 1 | 6 June 2011
- Weakly coupled systems of nonlinear elliptic boundary value problemsNonlinear Analysis: Theory, Methods & Applications, Vol. 6, No. 6 | 1 Jun 1982
- Large Amplitude Internal Waves of Permanent FormStudies in Applied Mathematics, Vol. 66, No. 1 | 28 September 2015
- Unique and Multiple Solutions of a Family of Differential Equations Modeling Chemical ReactionsSIAM Journal on Mathematical Analysis, Vol. 13, No. 1 | 17 July 2006
- Asymptotic stability of reaction-diffusion systems in chemical reactor and combustion theoryJournal of Mathematical Analysis and Applications, Vol. 82, No. 2 | 1 Aug 1981
- Comparison principles for reaction-diffusion systems: Irregular comparison functions and applications to questions of stability and speed of propagation of disturbancesJournal of Differential Equations, Vol. 40, No. 2 | 1 May 1981
- Stability and instability of the energy dependent diffusion system in reactor dynamicsMathematical Methods in the Applied Sciences, Vol. 3, No. 1 | 3 August 2011
- COMPARISON RESULTS FOR REACTION-DIFFUSION EQUATIONSRecent Advances in Differential Equations | 1 Jan 1981
- PARTICLE PROBLEMSThe Mathematical Understanding of Chemical Engineering Systems | 1 Jan 1980
- EMPTY TUBULAR AND FIXED-BED CATALYTIC REACTORSThe Mathematical Understanding of Chemical Engineering Systems | 1 Jan 1980
- ReferencesOperator Inequalities | 1 Jan 1980
- Multiple fixed point theorems for problems in chemical reactor theoryJournal of Mathematical Analysis and Applications, Vol. 69, No. 1 | 1 May 1979
- On the number of bounded positive solutions of the exterior elliptic boundary value problemsJournal of Mathematical Analysis and Applications, Vol. 67, No. 1 | 1 Jan 1979
- Boundary value problems for quasilinear second order elliptic equationsNonlinear Analysis: Theory, Methods & Applications, Vol. 2, No. 3 | 1 Mar 1978
- Inverse-monotone nonlinear differential operators of the second orderProceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 79, No. 3-4 | 14 November 2011
- Bounds for the solution of a non-linear parabolic initial-boundary value problemMathematical Proceedings of the Cambridge Philosophical Society, Vol. 82, No. 1 | 24 October 2008
- Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach SpacesSIAM Review, Vol. 18, No. 4 | 18 July 2006
- Positive solutions of a nonlinear boundary-value problem of parabolic typeJournal of Differential Equations, Vol. 22, No. 1 | 1 Sep 1976
- Some Mathematical Problems from NeurobiologyThe American Mathematical Monthly, Vol. 82, No. 9 | 11 April 2018
- Population growth described by a nonlinear boundary value problem of parabolic typeZeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 26, No. 4 | 1 Jul 1975
- Tubular Chemical Reactors: The “Lumping Approximation” and Bifurcation of Oscillatory StatesSIAM Journal on Applied Mathematics, Vol. 27, No. 3 | 12 July 2006
- Solutions of a Differential Equation Arising in Chemical Reactor ProcessesSIAM Journal on Applied Mathematics, Vol. 26, No. 4 | 12 July 2006
- Positive solution of a nonlinear diffusion system arising in chemical reactorsJournal of Mathematical Analysis and Applications, Vol. 46, No. 3 | 1 Jun 1974
- Stability analysis of the non-linear nuclear reactorInternational Journal of Control, Vol. 19, No. 3 | 27 March 2007
- Successive Approximations of Some Nonlinear Initial-Boundary Value ProblemsSIAM Journal on Mathematical Analysis, Vol. 5, No. 1 | 1 August 2006
- On the number of solutions of asymptotically superlinear two point boundary value problemsArchive for Rational Mechanics and Analysis, Vol. 55, No. 3 | 1 Jan 1974
- Multiple Solutions and Periodic Oscillations in Nonlinear Diffusion ProcessesSIAM Journal on Applied Mathematics, Vol. 25, No. 4 | 12 July 2006
- A discussion of critical parameters which can occur in frictionally heated non-newtonian fluid flowsInternational Journal of Heat and Mass Transfer, Vol. 16, No. 10 | 1 Oct 1973
- Some observations on uniqueness and multiplicity of steady states in non-adiabatic chemically reacting systemsThe Canadian Journal of Chemical Engineering, Vol. 51, No. 2 | 1 Apr 1973
- Variational solution and error bound for a nonlinear diffusion problem involving Arrhenius reaction ratesLettere Al Nuovo Cimento Series 2, Vol. 6, No. 7 | 26 November 2007
- A model equation arising from chemical reactor theoryArchive for Rational Mechanics and Analysis, Vol. 52, No. 4 | 1 Jan 1973
- Maximal and minimal solutions, effectiveness factors for chemical reaction in porous catalystsChemical Engineering Science, Vol. 28, No. 1 | 1 Jan 1973
- Remarks on the Existence Theory for Multiple Solutions of a Singular Perturbation ProblemSIAM Journal on Mathematical Analysis, Vol. 3, No. 3 | 17 February 2012
- Some problems concerning the non-adiabatic tubular reactor a-priori bounds, qualitative behavior, preliminary uniqueness and stability considerationsThe Canadian Journal of Chemical Engineering, Vol. 50, No. 4 | 1 Aug 1972
- Stability of solutions of nonlinear equationsJournal of Mathematical Analysis and Applications, Vol. 39, No. 1 | 1 Jul 1972
- Curvature functions for 2-manifolds with negative Euler characteristicBulletin of the American Mathematical Society, Vol. 78, No. 4 | 1 Jul 1972
- Multiple Solutions of Singular Perturbation ProblemsSIAM Journal on Mathematical Analysis, Vol. 3, No. 1 | 17 February 2012
- Existence Theory for Multiple Solutions of a Singular Perturbation ProblemSIAM Journal on Mathematical Analysis, Vol. 3, No. 1 | 17 February 2012
- Inverse Problems Connected with Two-Point Boundary Value ProblemsSIAM Journal on Applied Mathematics, Vol. 20, No. 3 | 12 July 2006