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

The author of this paper studies the existence of local minimum point of functional φφ in the first, and then the existence of homoclinic solutions to a pp-Laplacian system ddt[|u′(t)|p−2u′(t)]=∇F(t,u(t))+f(t) is investigated. Under local condition F(t,x)≥F(t,0)+b0|x|μ for all (t,x)∈R×Rn with |x|≤ρF(t,x)≥F(t,0)+b0|x|μ for all (t,x)∈R×Rn with |x|≤ρ, where b0>0,ρ>0b0>0,ρ>0 and μ>1μ>1 are constants, some new results are obtained.