关键词: locally Lipschitz potential,  generalized subdifferential,  coercive functional,  critical point,  local linking theorem,   , nonsmooth Palais-Smale condition,  multiple nontrivial solutions

Abstract:

We study nonautonomonus second order periodic systems with a nonsmooth potential. Using the nonsmooth critical theory, we establish the existence of at least two nontrivial solutions. Our framework incorporates large classes of both subquadratic and superquadratic potentials at infinity.

Key words: locally Lipschitz potential,  generalized subdifferential,  coercive functional,  critical point,  local linking theorem,   , nonsmooth Palais-Smale condition,  multiple nontrivial solutions