Nonlinear Elliptic Equations Of Non-trivial Solution

This dissertation is concerned with the existence and multiplicity of nontrivial solutions for a few kinds of nonlinear differential equations by appying critical point theory and variational methods. It mainly consists of four parts.In Chapter 2, we study by applying Morse theory and minimax methods the multiplicity of nontrivial solutions of semilinear elliptic boundary value problemwhereΩ(?) R~N is a bounded domain with smooth boundary (?)Ωand f∈C~1((?)×R,R) possesses certain increase conditions.In Chapter 3, a negative and a positive solution are obtained for the following modified capillary surface equationwhere p > 1,Ωis a bounded domain in R~N with smooth boundary.In Chapter 4, we study by variational methods the existence of nontrivial solitary waves of the generalized Kadomtsev-Petviashvili equationIn the final chapter, we study a non-homogeneous quasilinear elliptic equation on the Orlicz-Sobolev space setting and obtain the existence of infinitely many solutions.