Method of quasi-upper and lower solutions in abstract cones

DOI10.1016/0362-546X(82)90067-0zbMath0497.34047MaRDI QIDQ3961819

Aghalaya S. Vatsala, Vangipuram Lakshmikantham, S. G. Leela

Publication date: 1982

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

zbMATH Keywords

Banach spacemonotone iterative techniquecoupled extremal quasi-solutionsmethod of lower solutionmethod of upper solutions

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20)

Related Items (13)

A note on the theorem of Lakshmikantham and Leela ⋮ A monotone iterative scheme for nonlinear reaction-diffusion systems having nonmonotone reaction terms ⋮ Mixed monotone iterative technique for impulsive periodic boundary value problems in Banach spaces ⋮ Monotone iterative scheme for nonlinear hyperbolic boundary value problem ⋮ Monotone method for equations describing transport phenomena in a Banach space ⋮ Iterative solutions of systems of operator equations in ordered banach spaces and applications ⋮ Iterative method for coupled quasi-solutions of mixed monotone operator equations ⋮ Mixed monotone iterative technique for a class of semilinear impulsive evolution equations in Banach spaces ⋮ A method of L-quasi-upper and lower solutions for boundary value problems of impulsive differential equation in Banach spaces ⋮ Positive solutions for nonlinear integro-differential equations of mixed type in Banach spaces ⋮ Special issue: Lakshmikantham's legacy: a tribute on his 75th birthday ⋮ A brief biography and survey of collected works of V. Lakshmikantham ⋮ Application of the monotone-iterative techniques of V. Lakshmikantham for solving the initial value problem for impulsive differential-difference equations

Cites Work

• Monotone iterative technique for differential equations in a Banach space
• Existence and comparison theorems for differential equations in Banach spaces
• Sample solutions of stochastic ordinary differential equations^∗
• Quasi-solutions, vector Lyapunov functions, and monotone method
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• Unnamed Item

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