Weak homoclinic solutions of anisotropic discrete nonlinear system with variable exponent

Abstract

We prove the existence of weak solutions for an anisotropic homoclinic discrete nonlinear system. Suitable Hilbert spaces and norms are constructed. The proof of the main result is based on a minimization method. We also extend the problem by using generalized penality and source functions.

Keywords

• critical point theory
• discrete p(.)−laplacian system
• weak homoclinic solutions
• 47a75
• 35b38
• 35p30
• 34l05
• 34l30
• 39a70
• 35b20