Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential Original Research Article

A new result for the existence of homoclinic orbits is obtained for the second-order Hamiltonian system View the MathML sourceü(t)=∇F(t,u(t))+f(t), where t∈Rt∈R, u∈Rnu∈Rn, F∈C1(R×Rn,R)F∈C1(R×Rn,R) is TT-periodic with respect to tt, T>0T>0 and f:R→Rnf:R→Rn is a continuous and bounded function. This result generalizes and improves some known results in the previous literature.