Quasi-solutions and their role in the qualitative theory of differential equations

DOI10.1016/0362-546X(80)90066-8zbMath0449.34007MaRDI QIDQ3895823

Klaus Deimling, Vangipuram Lakshmikantham

Publication date: 1980

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

parabolic systemscomparison theoremsextremal solutionsvector Lyapunov functionsquasi-solutionssecond order boundary value problemsstability of Large Scale Systems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Differential inequalities involving functions of a single real variable (34A40)

Related Items (15)

Monotone-iterative method for solving the periodic problem for systems of impulsive differential equations ⋮ Variation of constants, vector Lyapunov functions, and comparison theorem ⋮ Quasi-solutions and monotone method for systems of nonlinear boundary value problems ⋮ Asymptotic stability of reaction-diffusion systems in chemical reactor and combustion theory ⋮ Existence of multiple quasifixed points of mixed monotone operators by iterative techniques ⋮ Nonlinear neutron diffusion with poisoning effects ⋮ Contributions to the fixed point theory of diagonal operators ⋮ Stability results for solutions of reaction diffusion systems by the method of quasisolutions^† ⋮ Special issue: Lakshmikantham's legacy: a tribute on his 75th birthday ⋮ A brief biography and survey of collected works of V. Lakshmikantham ⋮ A new extension of classical Müller's theorem ⋮ Quasi-solutions and monotone method for infinite systems of nonlinear boundary value problems ⋮ Monotone iterative methods for differential systems with finite delay ⋮ Application of the monotone-iterative techniques of V. Lakshmikantham for solving the initial value problem for impulsive differential-difference equations ⋮ Existence of coupled quasi-solutions of systems of nonlinear elliptic boundary value problems

Cites Work

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• An introduction to nonlinear boundary value problems
• On existence of extremal solutions of differential equations in Banach spaces
• Existence and comparison theorems for differential equations in Banach spaces
• $L_2 $-Stability and -Instability of Large-Scale Systems Described by Integrodifferential Equations
• Survey of decentralized control methods for large scale systems
• Stability of large-scale nonlinear systems--Quadratic-order theory of composite-system method using M-matrices

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