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

Huang Qi, Dong Yujun


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.


Sturm-Liouville BVPs; Duffing equations; limiting cases of asymptotically positive linear conditions; Fučik spectrum; existence of solutions; homotopy continuation methods

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