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

TL;DR

This paper investigates the asymptotic behavior and multiplicity of solutions for nonlinear elliptic equations with fractional Laplacians, extending classical results to nonlocal operators and critical exponents.

Contribution

It provides new insights into the asymptotic analysis and existence of multiple solutions for fractional Laplacian problems, a nonlocal extension of classical elliptic theory.

Findings

Characterization of asymptotic behavior of solutions

Existence of multiple bubbling solutions

Extension of classical results to fractional Laplacians

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).