2020年2月
Stable standing waves of nonlinear Schrodinger equations with potentials and general nonlinearities
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
- ,
- 巻
- 59
- 号
- 2
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/s00526-020-1703-0
- 出版者・発行元
- SPRINGER HEIDELBERG
The existence and nonexistence of the minimizer of the L-2-constraint minimization problem e(alpha) := inf{E(u)vertical bar u is an element of H1(RN), parallel to u parallel to(2)(L2(RN)) = alpha} are studied. Here,E(u) := 1/2 integral(RN) vertical bar del u vertical bar(2) + V(x)vertical bar u vertical bar(2)dx - integral(RN) F(vertical bar u vertical bar)dx,V(x) is an element of C(R-N), 0 not equivalent to V(x) <= 0, V(x) -> 0 (vertical bar x vertical bar -> infinity) and F(s) = integral(s)(0) f (t)dt is a rather general nonlinearity. We show that there exists alpha(0) >= 0 such that e(a) is attained for alpha > alpha(0) and e(alpha) is not attained for 0 < alpha < alpha(0). We study differences between the cases V(x) not equivalent to 0 and V(x) = 0, and obtain sufficient conditions for alpha(0) = 0. In particular, if N = 1, 2, then alpha(0) = 0, and hence e(alpha) is attained for all alpha > 0.
- リンク情報
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- DOI
- https://doi.org/10.1007/s00526-020-1703-0
- Web of Science
- https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000514176600001&DestApp=WOS_CPL
- Scopus
- https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079392541&origin=inward
- Scopus Citedby
- https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85079392541&origin=inward
- ID情報
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- DOI : 10.1007/s00526-020-1703-0
- ISSN : 0944-2669
- eISSN : 1432-0835
- SCOPUS ID : 85079392541
- Web of Science ID : WOS:000514176600001