Limiting cases of asymptotically positive linear conditions and solvability of Sturm-Liouville boundary-value problems of Duffing equations

Abstract

In this paper we study the solvability of Sturm-Liouville BVPs for Duffing equations by means of homotopy continuation methods. We propose a new kind of solvable conditions on the nonlinear function in the equation. This kind of conditions can be seen as some limiting cases of the well-known asymptotically positive linear conditions. The obtained results generalize and unify some previous results by S. Villegas, T. Ma and L. Sanchez, and Y. Dong, respectively.