Existence of positive solutions for p-Laplacian impulsive boundary value problems on time scales

Fatma Tokmak,Ilkay Y Karaca

doi:10.1186/1029-242x-2014-196

Abstract

In this paper, by using fixed point index theory and a double fixed point theorem, we study the existence of many positive solutions for a class of second-order p-Laplacian boundary value problems with impulse on time scales. An example which supports our theoretical results is also indicated.MSC:34B18, 34B37, 34K10.

Highlights

1 Introduction It is well known that the theory of impulsive differential equations has become more important in recent years in some mathematical models of real processes and phenomena
In Section, we provide some necessary background about time scales, the theory of cones in Banach space and some preliminary lemmas
Let us define the increasing, nonnegative, continuous functionals γ , β, and α on K by γ (u) = min u(t) = u(ξ ), t∈[ ,ξ ]T

Summary

Introduction

It is well known that the theory of impulsive differential equations has become more important in recent years in some mathematical models of real processes and phenomena. The authors considered impulsive boundary value problems without p-Laplacian and time scales in [ , ]. Motivated by the above results, in this study we consider the following second-order impulsive boundary value problem (BVP) on time scales:

Results

Conclusion