Generalized Nonsmooth Saddle Point Theorem and its applications on second order Hamiltonian systems

摘要

Highlights?The Generalized Nonsmooth Saddle Point Theorem is firstly proved.?Different critical point theorem for finding the solution is used.?Periodic bouncing solution forx¨=f(t,x)with our new conditions is studied.AbstractThe Generalized Nonsmooth Saddle Point Theorem is proved, which generalizes the previous ones. As its application, we obtain the existence of nontrivial periodic bouncing solution for systemsx¨=