Homoclinic orbits for second order nonlinear p-Laplacian difference equations

Existence of homoclinic orbits for a higher order difference system

“…In many studies (see, e.g., [3,4,9,11,12,14,15,23]) of second order difference equations, the following classical Ambrosetti-Rabinowitz condition is assumed (AR) there exists a constant β > 2 such that 0 < βF(k, u) uf(k, u) for all k ∈ Z and u ∈ R \ {0}.…”

Homoclinic solutions for second order discrete p-Laplacian systems

“…On the other hand, we know that a differential equation model is often derived from a difference equation, and numerical solutions of a differential equation have to be obtained by discretizing the differential equation, therefore, the study of periodic solution and connecting orbits of difference equation is meaningful [12][13][14][15][16][17][18][19][20][21][22][23][24].…”