A variant of Clark’s theorem and its applications for nonsmooth functionals without the global symmetric condition

Abstract

We give a new non-smooth Clark’s theorem without the global symmetric condition. The theorem can be applied to generalized quasi-linear elliptic equations with small continous perturbations. Our results improve the abstract results about a semi-linear elliptic equation in Kajikiya [10] and Li-Liu [11].

Keywords

• quasi-linear elliptic equations
• non-smooth clark’s theorem
• essential values
• 35j20
• 35j62
• 35b45