Research On The Existence Of Solutions To Boundary Value Problems For A Class Of Superlinear Elliptic Equations With Perturbation Terms

In this paper,the existence and multiple of solutions for a class of superlinear elliptic equation with perturbation terms are discussed,by means of calculus of variation?Nehari manifold theory and critical point theory,where ?(?)Rn is a bounded smooth domain,? is a constant,h(x)?L2(?),f(x,u)?C1(?×R),F(x,u)=?0 t f(x,s)ds.Here ?<?1,where ?1 denotes the first Dirichlet eigenvalue of(-?,H01(?)),according to Poincare inequality,We mainly consider the solution for h?0 and ??|h(x)|2dx being sufficiently small,we may assume that ? =0,and consider the existence of critical points of functional which can be regard as the classical solution to the above are elliptic equation.The paper consists of four chapters,of which contents can be stated as follows:The first chapter introduces the background of the study,researching significance,and the latest progress both at home and abroad,At the end of this chapter,the main results and innovations of this paper are given.The second chapter introduces some related knowledge of critical point theorem.The third chapter constructs a generalized manifold Nh,proves that the minimization sequence.{uk}(?)Nh of functional ?(u)is bounded and the infimum mh of functional ?(u)in manifold Nh is obtained.The fourth chapter gives the proof of the primary theorem A,obtaining two different nontrivial solutions for the elliptic partial differential equation with the perturbed terms.