Existence of Unbounded Positive Solutions of Boundary Value Problems for Differential Systems on Whole Lines

Abstract

This paper is concerned with integral type
boundary value problems of second order singular differential systems with
quasi-Laplacian operators on whole lines. A Banach space and a nonlinear completely continuous operator are defined. By using the Banach space and the nonlinear operator, together with the Schauder's fixed point theorem, sufficient
conditions to guarantee the existence of at least one unbounded positive solution
are established. Finally, we present a concrete example to illustrate the efficiency of the main theorem.