We obtain sufficient conditions for the existence of a nontrivial homoclinic solution to a second-order nonlinear difference equation with Jacobi operator. To do this, we use variational methods and critical point theory. An example is provided to illustrate our main result.
Submitted August 11, 2016. Published March 30, 2017.
Math Subject Classifications: 34C37, 37J45, 39A12, 47J22.
Key Words: Homoclinic solutions; nonlinear difference equations; Jacobi operators; critical point theory.
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| Fei Xia |
Central South University of Forestry and Technology
Changsha 410004, China
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