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