The method of upper, lower solutions and hyperbolic partial differential equations
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Publication:1061311
DOI10.1016/0022-247X(85)90062-9zbMath0569.35056MaRDI QIDQ1061311
Vangipuram Lakshmikantham, Sudhakar G. Pandit
Publication date: 1985
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)
Related Items (21)
On the Cauchy problem for linear hyperbolic functional-differential equations ⋮ Existence and attractivity for the Darboux problem of fractional order neutral differential equations ⋮ A monotone method for the equation \(u_{xyz}=f\) ⋮ Darboux problem for impulsive partial hyperbolic differential equations of fractional order with variable times and infinite delay ⋮ Partial neutral functional integro-differential equations of fractional order with delay ⋮ On nonlinear integro-differential equations of hyperbolic type ⋮ Linear hyperbolic functional-differential equations with essentially bounded right-hand side ⋮ Multiple solutions of a class of nonlinear hyperbolic problems ⋮ Carathéodory solutions to a hyperbolic differential inequality with a non-positive coefficient and delayed arguments ⋮ Unique solvability of the Darboux problem for linear hyperbolic functional differential equations ⋮ Periodic solutions of hyperbolic partial differential equations ⋮ Unnamed Item ⋮ Global uniqueness results for fractional order partial hyperbolic functional differential equations ⋮ Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order ⋮ Some remarks on linear functional differential inequalities of hyperbolic type ⋮ Existence results for impulsive hyperbolic differential inclusions ⋮ Special issue: Lakshmikantham's legacy: a tribute on his 75th birthday ⋮ A brief biography and survey of collected works of V. Lakshmikantham ⋮ Darboux problem for perturbed partial differential equations of fractional order with finite delay ⋮ Theory and analysis of partial differential equations with a \(\psi \)-Caputo fractional derivative ⋮ Darboux problem for fractional-order discontinuous hyperbolic partial differential equations in Banach algebras
Cites Work
- Existence and monotone method for periodic solutions of first-order differential equations
- Existence of periodic solutions of semilinear parabolic equations and the method of upper and lower solutions
- Quasi-solutions and monotone method for systems of nonlinear boundary value problems
- Elliptic boundary value problems suggested by nonlinear diffusion processes
- Existence and comparison theorems for differential equations in Banach spaces
- Monotone methods for nonlinear boundary value problems in banach spaces
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