Homoclinic orbits for second order self-adjoint difference equations

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Multiple homoclinic solutions for the discrete p-Laplacian via critical point theory (2013, background): “Ma and Guo [18] introduced discrete coercive weight functions, which allow one to deal directly with infinite-dimensional Banach spaces preserving certain compactness properties bymeans of such spaces.”
Existence and uniqueness of solutions for a fractional boundary value problem on a graph (2014, background): “For more studies on homoclinic solutions for difference equations, we refer the reader to [1, 3, 4, 6, 7, 9, 11] and the references therein.”