Multiple Solutions For Semilinear Elliptic Equations Involving Concave And Critical Nonlinear Terms

In this thesis,we study the existence and qualitative properties of nontrivial solutions for some semilinear elliptic equations with concave and critical nonlinearities via Nehari manifold and the elliptic equations theories.The main contents are summarized as follows:In chapter 1,we briefly outline the background,the structure and the specific questions to be studied of the dissertation.In chapter 2,we mainly list the basic concepts and related theorems needed in the disserta-tion.In chapter 3,we consider the Dirichlet problem(E_?,a,b)in a bounded domain involving con-cave and critical nonlinearities,We have proved the equation has at least two positive solutions.In the last chapter,we consider the Dirichlet problem(E_?,b),by the dual fountain theorem,we obtain the existence of the infinitely solutions and the asymptotic convergence property of the critical values.