Asymptotic Behavior Of Singular Solutions And Multiple Solutions For Fractional Elliptic Equations

In this thesis, we investigate the asymptotic behavior of positive singular solutions to fractional elliptic equations and multiple solutions. This thesis is divided into three chapters.In chapter 1, we introduce the background of the problem and main results of the thesis.In chapter 2, we study the positive solutions to semilinear elliptic equations involving the fractional Laplacian where p≥ 1, Ω is an open bounded regular domain in (?)N(N> 2) containing the origin, and (-△)α with α ∈ (0,1) denotes the fractional Laplacian. We show that the asymptotic behavior of positive singular solutions is controlled by a radially symmetric solution with being a ball.In chapter 3, We are devoted to the study of the following non-local fractional equation in-volving critical nonlinearities where Ω is a smooth bounded domain of (?)N, N≥2α, (-△)α/2 is the fractional operator, α∈ (0,2), λ ∈ (0, λ1), λ1 is the eigenvalue of the Laplace operator (-△)α/2 in in and 2N/N-α is fractional sobolev critical exponent, we show that (0.0.2) possesses at least CatΩ(Ω) nontrivial solutions.