Normalized solutions to Schrodinger systems with linear and nonlinear couplings

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:506

Article

Yun, Zhaoyang^1,2  Zhang, Zhitao^1,2,3 

[1] Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[3] Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China

关键词: Nonlinear Schrodinger systems;    Normalized solutions;    Ekland variational principle;    Minimax principle;   

DOI  :  10.1016/j.jmaa.2021.125564

来源: Elsevier

【 摘 要 】

In this paper, we study important Schrodinger systems with linear and nonlinear couplings {-Delta u(1) - lambda(1)u(1) = mu(1)vertical bar u(1)vertical bar(p1-2)u(1) + r(1)beta vertical bar u(1)vertical bar(r1-2)vertical bar u(2)vertical bar(r2) + kappa(x)u(2) in R-N, -Delta u(2) - lambda(2)u(2) = mu(2)vertical bar u(2)vertical bar(p2-2)u(2) + r(2) beta vertical bar u(1)vertical bar(r1)vertical bar u(2)vertical bar(r2-2)u(2) + kappa(x)u(1) in R-N u(1) is an element of H-1 (R-N), u(2) is an element of H-1 (R-N), with the condition integral(RN) u(1)(2) - a(1)(2), integral(RN) u(2)(2) - a(2)(2), where N >= 2, mu(1), mu(2), a(1), a(2) > 0, beta is an element of R, 2 < p(1), p(2) < 2*, r(1), r(2) > 1, r(1) + r(2) < 2*,kappa(x) is an element of L-infinity(R-N) with fixed sign and lambda(1), lambda(2) are Lagrangian multipliers. We use Ekland variational principle to prove this system has a normalized radially symmetric solution for L-2-subcritical case when N >= 2, and use minimax method to prove this system has a normalized radially symmetric positive solution for L-2-supercritical case when N = 3, p(1) = p(2) = 4, r(1) = r(2) = 2. (C) 2021 Elsevier Inc. All rights reserved.

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