Singularly perturbed Neumann problem for fractional Schrödinger equations

This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrödinger equations with subcritical exponent. For some smooth bounded domain Ω ⊂ R n , our boundary condition is given by ∫ u ( x ) − u ( y ) | x − y | n + 2 s d y = 0 f o r x ∈ ℝ n ∖ Ω ¯ . We establ...

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Bibliographic Details
Published inScience China. Mathematics Vol. 61; no. 4; pp. 695 - 708
Main Author Chen, Guoyuan
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.04.2018
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematical analysis
Mathematics
Mathematics and Statistics
Neumann problem
Nonlinear equations
Schrodinger equation
Neumann problem
35B38
singular perturbation
35B25
35J61
nonlinear fractional Schrödinger equations
fractional Laplacian
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Summary:This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrödinger equations with subcritical exponent. For some smooth bounded domain Ω ⊂ R n , our boundary condition is given by ∫ u ( x ) − u ( y ) | x − y | n + 2 s d y = 0 f o r x ∈ ℝ n ∖ Ω ¯ . We establish existence of non-negative small energy solutions, and also investigate the integrability of the solutions on R n .
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-016-0420-2