Existence results for nonlinear impulsive qk-integral boundary value problems

EXISTENCE RESULTS FOR NONLINEAR IMPULSIVE qk-INTEGRAL BOUNDARY VALUE PROBLEMS

u(T ) = ∑m i=0 ∫ ti+1 ti g(s, u(s)) dqis, where Dqk are qk-derivatives (k = 0, 1, 2, . . . ,m), f, g ∈ C(J ×R, R), Ik ∈ C(R,R), J = [0, T ](T > 0), 0 = t0 < t1 < · · · < tk < · · · < tm < tm+1 = T , J ′ = J\{t1, t2, . . . , tm}, and ∆u(tk) = u(t + k ) − u(t − k ), u(t + k ) and u(t − k ) denote the right and the left limits of u(t) at t = tk (k = 1, 2, . . . ,m) respectively. The study of q-dif...

Existence results for a kind of fourth-order impulsive integral boundary value problems

In this paper we investigate the existence of solutions to a kind of fourth-order impulsive differential equations with integral boundary value conditions. By employing the Schauder fixed point theorem, we obtain sufficient conditions which ensure the system has at lease one solution. Also by using the contraction mapping theorem we get the uniqueness result. Finally an example is given to illu...

Existence Results for Nonlinear Boundary Value Problems of Fractional Integrodifferential Equations with Integral Boundary Conditions

Existence Results for Nonlinear Boundary-value Problems with Integral Boundary Conditions

In this paper, we investigate the existence of solutions for a second order nonlinear boundary-value problem with integral boundary conditions. By using suitable fixed point theorems, we study the cases when the right hand side has convex and nonconvex values.

Existence Results for Nonlinear Boundary Value Problems of Impulsive Fractional Integrodifferential Equations

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...