Existence And Multiplicity Of Solutions For The Nonlocal Elliptic Equations With Critical Exponential Growth

In this dissertation,we study the following kinds of nonlocal elliptic equations:nonhomogeneous nonlocal elliptic equations,weighted nonhomogeneous nonlocal ellip-tic equations,nonlocal elliptic equations with periodic potential and nonlocal elliptic equations with higher-order eigenvalue perturbations,and obtains the existence and mul-tiplicity of the solutions by variational method.In Chapter 1,we introduce the physical background and recent development of the nonlocal elliptic equations.Then we present the preliminary knowledge and main results obtained in the thesis.In Chapter 2,we obtain the existence and multiplicity of the solutions of nonhomo-geneous nonlocal elliptic equation where 0<?<2,h ?H-1(R2),h?0,F(u)=f0u f(s)ds.In Chapter 3,we obtain the existence and multiplicity of the solutions of weighted nonhomogeneous nonlocal elliptic equation where?>0,??0,2?+??2,h?H-1(R2),h?0.In Chapter 4,we obtain the existence of the solution of the following strongly indef-inite nonlocal elliptic equation where 0<?<2,V is a 1-periodic function for each xi,i=1,2,(?)?(-?+V)?(-?,0)?0.In Chapter 5,we obtain the existence of the solution of nonlocal elliptic equation where(?)is bounded with smooth boundary,0<?<2,?k denotes the ?th eigenvalue of(?)Finally,we give some problems that need further discussion.