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Existence of Small-Energy Solutions to Nonlocal Schrodinger-Type Equations for Integrodifferential Operators in R-N

Title
Existence of Small-Energy Solutions to Nonlocal Schrodinger-Type Equations for Integrodifferential Operators in R-N
Authors
Lee, Jun IkKim, Yun-HoLee, Jongrak
Ewha Authors
이종락
Issue Date
2020
Journal Title
SYMMETRY-BASEL
ISSN
2073-8994JCR Link
Citation
SYMMETRY-BASEL vol. 12, no. 1
Keywords
non-local integrodifferential operatorsDe Giorgi iterationmodified functional methodsdual fountain theorem
Publisher
MDPI
Indexed
SCIE; SCOPUS WOS
Document Type
Article
Abstract
We are concerned with the following elliptic equations: (-Delta)p,Ksu+V(x)

u

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.
DOI
10.3390/sym12010005
Appears in Collections:
연구기관 > 수리과학연구소 > Journal papers
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