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（τ）=a-bτγ-1,τ≥0,2<γ<2s*/2,2s*=6/（3-2s）,a-b/γ>0,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.