Solvability of boundary value problem for second order impulsive differential equations with one-dimensional p-Laplacian on whole line

The motivation for the present work stems from both practical and theoretical aspects. In fact, boundary value problems on the whole line arise quite naturally in the study of radially symmetric solutions of nonlinear elliptic equations modelling various physical phenomena such as unsteady flow of gas though a whole, porous media, and the theory of drain flows. The asymptotic theory of ordinary differential equations is an area in which there is great activity among a large number of investigators. In this theory, it is of great interest to investigate, in particular, the existence of solutions with prescribed asymptotic behavior, which are global in the sense that they are solutions on the whole line (half line). The existence of global solutions with prescribed asymptotic behavior is usually formulated as the existence of solutions of boundary value problems on the whole line (half line). In recent years, the existence of solutions of boundary value problems of the differential equations governed by nonlinear differential operator [Φ(u′)]′ = [|u′|p−2u′]′ has been studied by many authors, see [5, 7, 8, 9, 10, 11, 12, 13, 15, 17].