Homoclinic solutions for a nonlinear second order differential system with p-Laplacian operator

The author of this paper studies the existence of local minimum point of functional phi in the first, and then the existence of homoclinic solutions to a p-Laplacian system d/dt[vertical bar u'(t)vertical bar(p-2)u'(t)] = Delta F(t, u(t)) + f (t) is investigated. Under local condition F(t. x) >= F(t, 0) + b(0)vertical bar x vertical bar(mu) for all (t, x) is an element of R x R-n with vertical bar x vertical bar <= rho, where b(0) > 0, rho > 0 and mu > 1 are constants, some new results are obtained. (C) 2010 Elsevier Ltd. All rights reserved.