Existence of Homoclinic Orbits for a Singular Differential Equation Involving p-Laplacian

The efficient conditions guaranteeing the existence of homoclinic solutions to second-order singular differential equation withp-Laplacian (phi(p)(x '(t)))'+f(x '(t))+g(x(t))+(h(t)/1-x(t)) = e(t) are established in the paper. Here, phi(p)(s) = vertical bar s vertical bar(p-2)s, p > 1, f, g, h , e is an element of C(R, R) with h(t+T) = h(t). The approach is based on the continuation theorem for coincidence degree theory.