Study On The Existence Of Solutions For Two Classes Of Nonlocal Problems

This master’s thesis mainly studies the existence of two kinds of nonlocal problem solutions,which are divided into four chapters:In Chapter 1,firstly,the background and research status of Kirchhoff equation and fractional Choquard equation are described,and then the main results of this paper are introduced.In Chapter 2,we briefly introduce some of notations,definitions and related lemmas used in this article.In Chapter 3,we research nontrivial solution of the following Kirchhoff equations with sign-changing weight(?) where a,b>0,3<p<5,V(x)is a continuous and sign-changing function and is less than zero at infinity.The existence of at least one nontrivial solution to the above equation is proved by using the mountain pass theorem and Sobolev inequality.In Chapter 4,we study normalized solution of the following mass supercritical fractional Choquard equation with potential function (?) where N>3,s∈(0,1),α∈(N-2s,N),p ∈(1+α+2s/N,N+α/N-2s),μ is a Lagrange multiplie,the potential function V ∈C1(RN)disappears at infinity.When V satisfies some conditional assumptions,the use of split lemma and generalized the minimax method of normal existence of the above equation.