Existence of positive solutions for a class of BVPs in Banach spaces

Abstract

In this work, we use index xed point theory for perturbation of expan- sive mappings by l-set contractions to study the existence of bounded positive solutions for a class of two-point boundary value problem (BVP) associated to second-order nonlinear di erential equation on the positive half-line. The nonlin- earity, which may exhibit a singularity at the origin, is written as a sum of two functions which behave di erently. These functions, depend on the solution and its derivative, take values in a general Banach space and have at most polynomial growth. An example to illustrate the main results is given.