Homoclinic orbits of a class of second-order difference equations (Q714098)

The authors study the existence of homoclinic orbits of the second-order difference equation \(\Delta^2x(t-1)-L(t)x(t)+V_x'(t,x(t))=0\). After an introduction and some preliminary results, they use the variational method and the spectral theory of difference operators to investigate the existence of homoclinic orbits for the case that \(V(t,\cdot)\) is superquadratic and for the case that \(V(t,\cdot)\) is subquadratic. Furthermore, they provide two illustrative examples to justify their theory.