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Existence of Small-Energy Solutions to Nonlocal Schrodinger-Type Equations for Integrodifferential Operators in R-N
- Existence of Small-Energy Solutions to Nonlocal Schrodinger-Type Equations for Integrodifferential Operators in R-N
- Lee, Jun Ik; Kim, Yun-Ho; Lee, Jongrak
- Ewha Authors
- Issue Date
- Journal Title
- SYMMETRY-BASEL vol. 12, no. 1
- non-local integrodifferential operators; De Giorgi iteration; modified functional methods; dual fountain theorem
- SCIE; SCOPUS
- Document Type
- We are concerned with the following elliptic equations: (-Delta)p,Ksu+V(x)
p-2u=lambda f(x,u), where (-Delta)p,Ks is the nonlocal integrodifferential equation with 0<s<1<p<+infinity, sp<N the potential function V:RN ->(0,infinity) is continuous, and f:RNxR -> R satisfies a Caratheodory condition. The present paper is devoted to the study of the L infinity-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 infinity-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.
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