In this paper, we investigate the existence of at least one, two and three positive solutions to nonlinear second order m-point impulsive time scale boundary value problems on infinite intervals by using Krasnosel?skii fixed point theorem, Avery-Henderson theorem five functionals respectively.

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory: ⎧⎨ ⎩ x′′(t) = f(t, x(t), x′(t)), t ∈ [0, 1], t = tk, k = 1, 2,··· ,m Δx(tk) = Ik(x(tk)), k = 1, 2,··· ,m Δx′(tk) = Ik(x(tk), x ′(tk)), k = 1, 2,··· ,m x′(0) = αx′(ξ), x(1) = βx(η), (E) where 0 < ξ ≤ η < 1, α ≥ 0, β ≥ 0 a...

*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...

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using Leray-Schauder theory: ⎧⎨ ⎩ x′′(t) = f(t, x(t), x′(t)), t ∈ [0, 1], t = tk, k = 1, 2,··· ,m Δx(tk) = Ik(x(tk)), k = 1, 2,··· ,m Δx′(tk) = Ik(x(tk), x ′(tk)), k = 1, 2,··· ,m x(0) = αx(ξ), x′(1) = βx′(η), (E) where 0 < ξ ≤ η < 1, α ≥ 0, β ≥ 0 a...

A recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas is used to investigate the existence and uniqueness of solutions to first-order boundary value problems for impulsive functional differential equations with infinite delay. An example to illustrate the results is included.

This paper is concerned with the nonlinear boundary value problems for first order integro-differential equations with impulsive integral conditions. By using of the method of lower and upper solutions coupled with the monotone iterative technique, we give conditions for the existence of extremal solutions.

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:   x′′(t) = f(t, x(t), x′(t)), t ∈ [0, 1], t 6= tk, k = 1, 2,··· ,m ∆x(tk) = Ik(x(tk)), k = 1, 2,··· ,m ∆x′(tk) = Ik(x(tk), x ′(tk)), k = 1, 2,··· ,m x(0) = αx(ξ), x(1) = βx(η), (E) where 0 < ξ ≤ η < 0, αξ(1 − β) + (1 ...

In this paper, we investigate the existence result for nonlinear impulsive fractional integro-differential equations with boundary conditions by using fixed point theorem and Green's function. I. INTRODUCTION The topic of fractional differential equations has received a great deal of attention from many scientists and researchers during the past decades; see [1-7]. This is mostly due to the fac...