Existence of Small-Energy Solutions to Nonlocal Schrödinger-Type Equations for Integrodifferential Operators in ℝN

Abstract

We are concerned with the following elliptic equations:Carathéodory condition. The present paper is devoted to the study of the L ∞ -bound of solutions to the above problem by employing De Giorgi's iteration method and the localization method. Using this, we provide a sequence of infinitely many small-energy solutions whose L ∞ -norms converge to zero. The main tools were the modified functional method and the dual version of the fountain theorem, which is a generalization of the symmetric mountain-pass theorem.