Existence And Multiplicity Critical Points For Nonsmooth Functionals

In this paper, we discuss three topics by applying nonsmooth critical point theory. The first is infinitely many solutions for quasilinear elliptic equations in-RN; the second is infinitely many solutions for a class of quasilinear elliptic equations with p-Laplacian in RN; and the last is infinitely many critical points for a class of lower semicontinuous functionals in RN.The paper consists of four chapters. In chapter one, we mainly introduce the development of the nondifferentiable functionals, the significance of the issue and present stage of research. State the problems what we have solved in this paper. Furthermore, we introduce a synopsis of the main results from this paper. We also give some definitions, some fundamental lemmas and theorems.In chapter two, we discuss the multiplicity of solutions for the following quasilinear elliptic equation we will give some conditions to ?(x,u)such that the functional satisfies compactness condition.In chapter three, we deal with the existence of many solutions for the following quasilinear elliptic equation P is a given continuous function satisfyingIn Chapter four, we prove the existence of infinitely many solutions for the following quasilinear equation in RN. Here, we suppose that there exist a constant α0> 0 and a positive increasing function α∈C (R) such that...