Second-order Impulsive Boundary Value Problems Research Articles

Existence of Positive Solutions for Second-Order Impulsive Boundary Value Problems on Time Scales

In this paper, by using Leray–Schauder fixed-point theorem, Avery–Henderson fixed-point theorem and Leggett–Williams fixed-point theorem, respectively, we investigate the conditions for the existence of at least one, two and three positive solutions to nonlinear second-order impulsive boundary value problems on time scales.

Existence of Positive Solutions for Nonlinear Second-Order Impulsive Boundary Value Problems on Time Scales

This paper is concerned with the existence of positive solutions of second-order impulsive boundary value problem with integral boundary conditions on time scales. Existence results of at least three positive solutions are established via a new fixed point theorem in a cone. Also, an example is given to illustrate the effectiveness of our result.

Sign-Changing and Multiple Solutions of Impulsive Boundary Value Problems Via Critical Point Methods

In this paper, we study the second-order impulsive boundary value problem ? Lu = f ( x , u ) , x ? [ 0 , 1 ] ? { x 1 , x 2 , ? , x l } , ? Δ ( p ( x i ) u ? ( x i ) ) = I i ( u ( x i ) ) , i = 1 , 2 , ? , l , R 1 ( u ) = 0 , R 2 ( u ) = 0 , $$\left\{\begin{array}{ll} -Lu=f(x, u), \, \, x\in [0, 1]\backslash\{x_{1}, x_{2}, \cdots, x_{l}\}, \\ -{\Delta} (p(x_{i}) u'(x_{i}))=I_{i}(u(x_{i})), \quad i=1, 2, \cdots, l, \\ R_{1}(u)=0, \, \, \, R_{2}(u)=0, \end{array}\right.$$ where Lu = (p(x)u?)? ? q(x)u is a Sturm-Liouville operator, R 1(u) = ?u?(0) ? βu(0) and R 2(u) = ?u?(1) + ?u(1). The existence of sign-changing and multiple solutions is obtained. The technical approach is based on minimax methods and invariant sets of descending flow.

Existence results for second-order impulsive boundary value problems on time scales

In this paper, using a fixed point theorem due to Krasnoselskii and Zabreiko and the Leggett–Williams fixed point theorem respectively, we investigate the existence of one solution and three nonnegative solutions to second-order impulsive equations on time scales.

On a class of second‐order impulsive boundary valueproblem at resonance

We consider the following impulsive boundary value problem, x″(t) = f(t, x, x′), t ∈ J\{t1, t2, …, tk}, Δx(ti) = Ii(x(ti), x′(ti)), Δx′(ti) = Ji(x(ti), x′(ti)), i = 1, 2, …, k, x(0) = (0), . By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than recent results. Our results extend some work concerning the usual m‐point boundary value problem at resonance without impulses.

Existence of positive solution for second-order impulsive boundary value problems on infinity intervals

We deal with the existence of positive solutions to impulsive second-order differential equations subject to some boundary conditions on the semi-infinity interval.