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

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