The Existence Of Solutions To Two Types Of Fractional P-Laplacian Differential Equations With Critical Exponential Growth And Decay Potential

In this paper,several kinds of fractional elliptic partial differential equations with critical exponential growth are studied by variational method.The existence and concentration 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 to a class of fractional p-Laplace equations with critical exponents whose potential function can decay to zero at infinity.By establishing the corresponding embedding theorem on the weight function space.We can get that the above equation has at least one positive solution by applying variational method.In Chapter 3,We study the existence and concentration of solutions for fractional p-Laplace equations with critical exponents and competing potential functions.By using variational method,concentration-compactness principle,Moser iteration method and penalization function method,we prove the existence and concentration of positive solutions under certain conditions.