Existence of coupled quasi-solutions of systems of nonlinear reaction- diffusion equations

DOI10.1016/0022-247X(85)90022-8zbMath0589.35061OpenAlexW2068487005MaRDI QIDQ1074022

Vangipuram Lakshmikantham, Aghalaya S. Vatsala, Gangaram S. Ladde

Publication date: 1985

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(85)90022-8

zbMATH Keywords

minimal and maximal solutionscoupled extremal quasi- solutionssystems of nonlinear reaction-diffusion problems

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Theoretical approximation in context of PDEs (35A35) Initial value problems for linear higher-order PDEs (35G10) Diffusion and convection (76R99) Higher-order parabolic equations (35K25)

Related Items (13)

Enclosure results for quasilinear systems of variational inequalities ⋮ Multiple positive solutions for a critical quasilinear elliptic system ⋮ Shape-invariant bounds for reaction-diffusion systems with unequal diffusion coefficients ⋮ A monotone iterative scheme for nonlinear reaction-diffusion systems having nonmonotone reaction terms ⋮ Pointwise bounds for linear reaction-diffusion systems and an extension to nonlinear problems ⋮ Nonlinear elliptic systems in unbounded domains ⋮ Multiple nontrivial solutions for critical growth quasilinear elliptic systems ⋮ Multiple positive solutions for a critical elliptic system with concave and convex nonlinearities ⋮ Monotone enclosure for elliptic and parabolic systems wit nonmonotone nonlinearities ⋮ Special issue: Lakshmikantham's legacy: a tribute on his 75th birthday ⋮ A brief biography and survey of collected works of V. Lakshmikantham ⋮ Petrov-Galerkin methods for systems of nonlinear reaction-diffusion equations ⋮ Multiple positive solutions for semi‐linear elliptic systems involving sign‐changing weight

Cites Work

• On nonlinear reaction-diffusion systems
• Existence and multiplicity theorems for semi-linear elliptic boundary value problems
• Invariant sets and the Hukuhara-Kneser property for systems of parabolic partial differential equations
• Asymptotic behavior and nonexistence of global solutions for a class of nonlinear boundary value problems of parabolic type
• Existence of coupled quasi-solutions of systems of nonlinear elliptic boundary value problems
• A monotone method for a system of nonlinear parabolic differential equations
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• On the Existence of Maximal and Minimal Solutions for Parabolic Partial Differential Equations
• A priori estimates for second-order parabolic equations
• Equivalent Norms for Sobolev Spaces
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