Singularly perturbed Neumann problem for fractional Schrdinger equations

被引：0

作者：

Guoyuan Chen ^{[1
]}

机构：

[1] School of Data Sciences, Zhejiang University of Finance & Economics

来源：

Science China(Mathematics) | 2018年 / 61卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Neumann problem; nonlinear fractional Schrdinger equations; singular perturbation; fractional Laplacian;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrdinger equations with subcritical exponent. For some smooth bounded domain ?  R~n, our boundary condition is given by∫?u(x)-u(y)/|x-y|n+2sdy = 0 for x ∈ R~n\?.We establish existence of non-negative small energy solutions, and also investigate the integrability of the solutions on Rn.

引用

页码：695 / 708

页数：14

共 50 条

[41] Singularly Perturbed Optimal Tracking Problem
Sobolev, V. A.
DIFFERENTIAL EQUATIONS, 2024, 60 (04) : 533 - 549
[42] A singularly perturbed Neumann problem for the Poisson equation in a periodically perforated domain. A functional analytic approach
Lanza de Cristoforis, Massimo
Musolino, Paolo
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2016, 96 (02): : 253 - 272
[43] Least energy solutions of nonlinear Schrödinger equations involving the fractional Laplacian and potential wells
MiaoMiao Niu
ZhongWei Tang
Science China Mathematics, 2017, 60 : 261 - 276
[44] Necessary and Sufficient Conditions for the Solvability of the Neumann and the Regularity Problems in Lp of Some Schrödinger Equations on Lipschitz Domains
Sibei Yang
Potential Analysis, 2018, 49 : 527 - 554
[45] Fractional Schrödinger Equation in Bounded Domains and Applications
Mohamed Ben Chrouda
Mediterranean Journal of Mathematics, 2017, 14
[46] Existence of the Gauge for Fractional Laplacian Schrödinger Operators
Michael W. Frazier
Igor E. Verbitsky
The Journal of Geometric Analysis, 2021, 31 : 9016 - 9044
[47] Multiple solutions to a perturbed Neumann problem
Cordaro, Giuseppe
STUDIA MATHEMATICA, 2007, 178 (02) : 167 - 175
[48] A kind of singularly perturbed boundary value problem for nonlinear Volterra functional differential equations
Lu S.
Applied Mathematics-A Journal of Chinese Universities, 2000, 15 (2) : 137 - 142
[49] DIFFERENCE SCHEMES FOR THE SINGULARLY PERTURBED SOBOLEV EQUATIONS
Amiraliyev, G. M.
Amiraliyeva, I. G.
DIFFERENCE EQUATIONS, SPECIAL FUNCTIONS AND ORTHOGONAL POLYNOMIALS, 2007, : 23 - 40
[50] Algebraic foundations of the theory of singularly perturbed equations
V. I. Kachalov
Doklady Mathematics, 2012, 85 : 161 - 162

← 1 2 3 4 5 →