Homoclinic Solutions for the Kirchhoff-type Difference Equations with Periodic Coefficients
By means of critical point theory,we investigate homoclinic solution problems for the Kirchhoff-type difference equations with periodic coefficients.First,we verify that the graph of the energy functional satisfies the mountain pass geometrical properties.Such mountain pass geometry produces a Palais-Smale sequence.Second,we exploit one global property condition to guarantee that this Palais-Smale sequence is bounded.Further,by using the subset of l2 consisting of functions with compact support and periodicity of coefficients,we obtain the existence of one nontrivial homoclinic solution for the Kirchhoff-type difference equations with periodic coefficients.Finally,two examples are given to illustrate our main results.
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