Research On The Existence Of Solutions To Several Types Of Fractional Elliptic Equations With Critical Exponential Growth

In this paper,we apply critical point theory to study several fractional elliptic partial differential equations with critical exponential growth.The existence and multiplicity of their solutions are discussed respectively.In Chapter 1,we briefly describe the research background,research status,main research results and innovations of this paper.In Chapter 2,we study the existence of solutions for a class of fractional equation with critical exponent and sign-changing weight function.We prove that there are two nontrivial solutions for the equation under certain conditions by Nehari manifold decomposition method and energy estimation.In Chapter 3,we study the existence of solutions for a class of fractional elliptic equations with critical exponents and Hardy potential.Similarly,we use Nehari manifold method and global compactness principle by constructing k-compact sequences to prove that the equation has k+1 nontrivial solutions under certain conditions.