Method of upper and lower solutions for second-order impulsive integro-differential equations in a Banach space

DOI10.1016/S0898-1221(99)00196-0zbMath0939.45004MaRDI QIDQ1963105

Dajun Guo, Xinzhi Liu

Publication date: 20 January 2000

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

upper and lower solutionsinitial value problemBanach spacemaximal and minimal solutionssecond-order nonlinear impulsive integro-differential equations of Volterra type

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Other nonlinear integral equations (45G10) Abstract integral equations, integral equations in abstract spaces (45N05) Theoretical approximation of solutions to integral equations (45L05)

Related Items (22)

On well-posedness of an initial value problem for nonlinear second-order impulsive integro-differential equations of Volterra type in Banach spaces ⋮ Half-linear impulsive problems for classical and singular \(\phi \)-Laplacian with generalized impulsive conditions ⋮ Transformation technique, fixed point theorem and positive solutions for second-order impulsive differential equations with deviating arguments ⋮ Convergence of solutions for functional integro-differential equations with nonlinear boundary conditions ⋮ Existence and continuity of positive solutions on a parameter for second-order impulsive differential equations ⋮ Comparison results for initial value problems of second-order impulsive integro-differential inclusions ⋮ Nontrivial convex solutions on a parameter of impulsive differential equation with Monge-Ampère operator ⋮ Positive solutions for Neumann boundary value problems of second-order impulsive differential equations in Banach spaces ⋮ On the existence of nonnegative radial solutions for Dirichlet exterior problems on the Heisenberg group ⋮ A class of \(n^{\text{th}}\)-order impulsive integrodifferential equations in Banach spaces. ⋮ Eigenvalues of a class of singular boundary value problems of impulsive differential equations in Banach spaces ⋮ Professor Dajun Guo: a true mathematician and educator ⋮ Positive solutions of an infinite boundary value problem for \(n\)th-order nonlinear impulsive singular integro-differential equations in Banach spaces ⋮ Parameter dependence of positive solutions for second-order singular Neumann boundary value problems with impulsive effects ⋮ Multiple solutions for sub-linear impulsive three-point boundary value problems ⋮ Transformation techniques and positive solutions on a parameter for three-point impulsive differential equations ⋮ Extremal solutions for \(n\)th-order impulsive integro-differential equations on the half-line in Banach spaces ⋮ Transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations ⋮ Positive solutions for \(n\)th-order nonlinear impulsive singular integro-differential equations on infinite intervals in Banach spaces ⋮ Multiple positive solutions of a boundary value problem for nth-order impulsive integro-differential equations in Banach spaces ⋮ Sharp conditions for the existence of positive solutions for a second-order singular impulsive differential equation ⋮ On higher order nonlinear impulsive boundary value problems

Cites Work

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