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Existence of homoclinic solutions for a nonlinear fourth order $ p $-Laplacian difference equation

  • * Corresponding author: Nikolay Dimitrov

    * Corresponding author: Nikolay Dimitrov 
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  • The aim of this paper is the study of existence of homoclinic solutions for a nonlinear difference equation involving $ p $-Laplacian. Under suitable growth conditions we prove that the considered problem has at least one homoclinic solution. The proof is based on the mountain-pass theorem with Cerami's condition, Brezis-Lieb lemma and variational method.

    Mathematics Subject Classification: Primary: 34B15, 34C37; Secondary: 39A10.


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