Research On The Existence Of Solutions To Several Types Of Fractional Elliptic Equations

In this paper,we apply critical point theory to study some nonlocal elliptic partial differential equations aiming to establish the multiplicity and the existence of least energy sign-changing solution,respectively.Chapter 1 is introduction,we introduce the research background and the current state and progress of this dissertation.We sketch its main results and innovation.In the second chapter,we are to prove multiplicity of solutions for nonlocal equation M(??R3×R3|u(x)-u(y)|2 K(x-y)dxdy)Lxu-?u= f(x,u),The nonlinearity f satisfies natural superlinear and subcritical growth assumptions.Precisely,along this chapter we prove the existence of at least three non-trivial solutions for this problem in a suitable left neighborhood of any eigenvalue of-Lku ??u.For this purpose we employ a linking theorem of mixed type(one of the so-called ?-theorems).In the third chapter,we study a class of fractional Kirchhoff equation in a bounded domain with nonliearity having a subcritical growth.Using a minimization argument and a deformation lemma,we obtain a least energy sign-changing solution for this problem.