Sign Changing Solutions Of A P-Laplacian Elliptic Problem With Constraint In R~N

In this thesis, by using some basic approaches in variational methods such as minimax method, invariant sets of descending flow and the variational technique, we study the existence of the sign changing solutions of the following p-Laplacian elliptic problem with constraint in IR-RNIn chapter one, we recall some background knowledge and results of the related elliptic equation. We also discribe the problem we will study.In chapter two, we recall some basic knowledge and some lemmas of Sobolev spaces and critical point theory.In chapter three, by using the method of adding the potential, we get the space E and discuss the properties of the space E. Then we obtain the embedding Eâ†'Lq(RN), p≤q<p*is compact. So that we can prove that the energy function of the elliptic equation (Ip) satisfies P. S. condition.In chapter four, we construct a pseudo gradient vector field and establish a suitable invariant sets of descending flow so that all positive solutions and negative solutions are contained in these invariant sets of descending flow. Therefore, by using minimax principle, we can obtain the sign changing solutions of the elliptic problem (Ip) outside theose invariant sets of descending flow.