Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian

Abstract

In this paper we study the asymptotic behavior of least energy solutions and the existence of multiple bubbling solutions of nonlinear elliptic equations involving the fractional Laplacians and the critical exponents. This work can be seen as a nonlocal analog of the results of Han (Ann. Inst. H. Poincare Anal. Non Lineaire, 1991) and Rey (J. Funct. Anal., 1990).

Parts of Section 1, 3, 4 and 6 are revised, and typos are fixed. To appear in Journal of Functional Analysis