Solutions for the Problems Involving Fractional Laplacian and Indefinite Potentials

Abstract

In this paper, we consider a class of Schrödinger equations involving fractional Laplacian and indefinite potentials. By modifying the definition of the Nehari–Pankov manifold, we prove the existence and asymptotic behavior of least energy solutions. As the fractional Laplacian is nonlocal, when the bottom of the potentials contains more than one isolated components, the least energy solutions may localize near all the isolated components simultaneously. This phenomenon is different from the Laplacian.

Keywords

• fractional laplacian
• least energy solutions
• indefinite potentials
• 35j60
• 35j20