Existence, Asymptotics and Computation of Solutions of Nonlinear Sturm-Liouville Problems

Abstract

This paper deals with the existence, asymptotics and computation of solutions of nonlinear Sturm-Liouville problems with general separated boundary conditions. The approach centers first on converting these problems into Hammerstein integral equations with modified argument, and then applying the Banach and Rothe fixed point theorems to solve them. This approach not only enabled us to prove existence theorems for these problems, but also to derive general and accurate asymptotic formulae for their solutions. Finally, an illustrative numerical example is presented using the Picard’s iteration method.