Abstract
By the Leray-Schauder's degree, the existence of solutions for a weighted -Laplacian impulsive integro-differential system with multi-point and integral boundary value conditions is considered. The sufficient results for the existence are given under the resonance and nonresonance cases, respectively. Moreover, we get the existence of nonnegative solutions at nonresonance.
Highlights
In this paper, when p t is a general function, we investigate the existence of solutions and nonnegative solutions for the weighted p t -Laplacian impulsive integrodifferential system with multipoint and integral boundary value conditions
By solving for u in 2.5 and integrating, we find ut u0 ai F φ−1 t, w t −1 ρ1 bi F f t ti
As in the proof of Theorem 3.1, we know that all the solutions of u Φδ u, 0 are uniformly bounded, there exists a large enough
Summary
We consider the existence of solutions for the following weighted p t -Laplacian integrodifferential system:. There are many works devoted to the existence of solutions to the Laplacian impulsive differential equation boundary value problems, for example 20–28. Because of the nonlinearity of −Δp, results about the existence of solutions for p-Laplacian impulsive differential equation boundary value problems are rare see. In this paper, when p t is a general function, we investigate the existence of solutions and nonnegative solutions for the weighted p t -Laplacian impulsive integrodifferential system with multipoint and integral boundary value conditions. Our results contain both the cases of resonance and nonresonance, and the method is based upon Leray-Schauder’s degree.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
