Singular Boundary Value Problems For The Impulsive One-Dimensional P-Laplacian

In mordern technology areas of practial problems, impulse as an instantaneous catastrophe phenomenon is universal existence. Recentlly some new technology achievement has been proved that impulsive system universally existed in aeromau-tics,informatics,cybernetics,communicats,biology,medicine,economics areas.This paper is devoted to study the existence of positive solutions for the singular one-dimensional p-laplacian with impulse effects.This paper is composed of three parts. In the first chapter, we introduce the historical background of the problems which will be investigated and the main results of this paper. In the second chapter, we present an existence principle which will be needed in chapter three. In the third chapter, by employing Arzela-Ascoli theorem and Krasnoselskii fixed point theorem, they were proved the existence of positive solutions for the following singular p-laplacian with impulse effectsHere, letτ∈(0,1) be given, whereφ(s) = |s|^p-2s, p > 1, f(t,u)∈C((0,1)×(0,∞), (0,∞)), and nonlinearity f may be singular at u = 0; I : [0,∞)→[0,∞) is continuous and nondecreasing;△φ(u')|_t=τ=φ(u')(τ+0)-φ(u')(τ-0), whereφ(u')(τ+ 0) (respectively ,φ(u')(τ-0)) denote the right limit (respectively ,left limit) ofφ(u')(t) at t =τ.