Infinitely Many Solutions For A Class Of Sublinear Schrodinger Equations With Parameter

Consider a class of sublinear Schrodinger equation with parameter: whereu,L:RNâ†'R,f:RN x Râ†'R, paramenterλ∈R\{0},f:RN x Râ†'R.Consider two different assumptions about potential of problem (*):(LI) L is a Lebesgue measurable function on RN, and essinf L(x):=l>0;(L2)L∈Lq(RN), q satisfies: and there exists non-empty open set U(?)RN and constant l0<0so that L(x)≤l0, a.e.x∈U.In this thesis, we deal with the existence of infinitely many nontrivial solutions for problem (*) under the assumption (LI) or (L2). This thesis consists of five sections.In section one, we introduce the origin and research methods on problem (*), the framework and main contents in this thesis.In section two, we introduce the basic conceptions and theorems in the functional analysis and critical point theory.In section three, based on the mountain pass lemma and genus theorem, we deal with the existence of infinitely many nontrivial solutions for problem (*) under the assumption (LI).In section four, based on the variational principle, we deal with the existence of infinitely many nontrivial solutions for problem (*) under the assumption (L2).In section five, we give some examples for the results which we get in the section three and four.