Existence And Multiplicity Of Nontrivial Solutions For A Class Of Nonlocal Problems

This paper study the existence and multiplicity of nontrivial solutions for a class of nonlocal problems.The paper is structured as follows:Chapter 1 provides a brief overview of the research background,the current state of research,the formulation of the problem,and the preparatory knowledge.Chapter 2 studies a class of nonlocal problems of the following form:where,N>2s,s?(0,1),43,M(?)=a-b??-1,??0,20,a,b?R0+=[0,?).When f(x,u)satisfies the(AR)condition and does not,we prove the existence of infinitely many solutions to the problem using the Symmetric Mountain Pass Theorem.