Two Kinds Of Dirichlet Boundary Value Problems Of Nonlinear Differential Equations Without AR Condition

Boundary value problem for nonlinear differential equations is a class of very important issue. The research has made great progress and it is still active. Recently, the subject of boundary value problem of differential equations in which the nonlinearity does not satisfy AR condition has caused wide public concern. In this thesis, we discuss two kinds of Dirichlet boundary value problems of nonlinear differential equations without AR condition.In chapter1, the development and present situation of the relevant question are summarized briefly.In chapter2, by the Saddle Point Theorem, the least action principle and Mountain Pass Lemma we consider the existence of nontrivial solutions for Dirichlet boundary value problem of second order nonlinear elliptic equation without AR conditionwhere Ω is a bounded domain in Rn (n≥3) with smooth boundary (?)ΩIn chapter3, by a variant version of the Mountain Pass Lemma we consider the existence of nontrivial solutions for Dirichlet boundary value problem of p-Laplace (p>1) equation without AR conditionwhere Ω is a bounded domain in Rm{n≥3) with smooth boundary (?)Ω...