Solvability of boundary value problems for singular quasi-Laplacian differential equations on the whole line

Abstract

This paper is concerned with some integral type boundary value problems associated to second order singular differential equations with quasi-Laplacian on the whole line. The emphasis is put on the one-dimensional p-Laplacian term  involving a nonnegative function ρ that may be singular at t = 0 and such that . A Banach space and a nonlinear completely continuous operator are defined in this paper. By using the Schauder's fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established. An example is presented to illustrate the main theorem.