Existence of positive solutions for quasi-linear differential equations

Abstract

Sufficient conditions for the existence of at least one positive solution for the following quasilinear differential equation ( ϕ p ( x′))′ + c( t) f( x) = 0 are given, where ϕ p ( u) = | u| p−2 u, p ≥ 2 is a constant, c ϵ C( R +, R +), f( x) > 0 for x > 0, f( x) = 0 for x ≤ 0. The method used in this paper is the shooting method.