Research On The Existence Of Solutions For Two Classes Of Nonlocal Elliptic Problems

In this paper,we mainly use the Lyapunov-Schmidt reduction method to study the existence of solutions for two classes of nonlocal elliptic problems.The paper is divided into three chapters:In Chapter One,we summarize the background of the ralated problems and state the main results of the present thesis.We also give some preliminary results and notations used in the whole thesis.In Chapter Two,we study the following Schrodinger-Poisson systems with electromagnetic potentials Where 1<p<5,the potentials A(r)=A(|x|)=(A1(|x|),A2(|x|),A3(|x|)),V(r)=V(|x|)and Q(r)=Q(|x|)are radial.We obtain infinitely many non-radial complex-valued solutions for this system.In Chapter Three,we consider the following fractional Schrodinger equation Where N? 3,0<s<1,1<p<(N+2s)/(N-2s)and K(|x|)is a positive radial function.We constructed infinitely many non-radial solution of the new type which have a more complex concentration structure for the equation.