Basic Theory for Nonresonance Impulsive Periodic Problems of First Order

Resonance and Nonresonance Periodic Value Problems of First-Order Differential Systems

Existence of Solutions of Periodic Boundary Value Problems for Impulsive Functional Duffing Equations at Nonresonance Case

This paper deals with the existence of solutions of the periodic boundary value problem of the impulsive Duffing equations: x′′ t αx′ t βx t f t, x t , x α1 t , . . . , x αn t , a.e. t ∈ 0, T , Δx tk Ik x tk , x′ tk , k 1, . . . , m, Δx′ tk Jk x tk , x′ tk , k 1, . . . , m, x i 0 x i T , i 0, 1. Sufficient conditions are established for the existence of at least one solution of above-mentioned ...

Existence result for impulsive third order periodic boundary value problems

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative te...

Periodic boundary value problems for first-order impulsive difference equations with time delay

*Correspondence: [email protected] 3Department of Mathematics, University of Hong Kong, Pokfulam, Hong Kong Full list of author information is available at the end of the article Abstract This paper focuses on a certain type of periodic boundary value problems for first-order impulsive difference equations with time delay. Notions of lower and upper solutions are introduced, with which two new co...

On Periodic Boundary Value Problems of First Order Discontinuous Impulsive Differential Inclusions

In this paper we prove existence results for extremal solutions of the first order discontinuous impulsive differential inclusions with periodic boundary conditions and impulses at the fixed times under certain monotonicity conditions of the multi-valued functions.