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Solutions of perturbed Schrodinger equations with critical nonlinearity
Ding, Yanheng; Lin, Fanghua
2007-10-01
Source PublicationCALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
ISSN0944-2669
Volume30Issue:2Pages:231-249
AbstractWe consider the perturbed Schrodinger equation {(u(x) -> 0) (-epsilon 2 Delta u + V(x)u = P(x)vertical bar u vertical bar p-2u + K(x)vertical bar u vertical bar 2*- 2u) (as vertical bar x vertical bar -> infinity) (for x epsilon RN) where N >= 3, 2* = 2N/(N - 2) is the Sobolev critical exponent, p epsilon (2, 2*), P(x) and K(x) are bounded positive functions. Under proper conditions on V we show that it has at least one positive solution provided that epsilon <= epsilon; for any m epsilon N, it has m pairs of solutions if epsilon <= epsilon(m); and suppose there exists an orthogonal involution tau : R-N -> R-N such that V(x), P(x) and K(x) are tau- invariant, then it has at least one pair of solutions which change sign exactly once provided that epsilon <= epsilon, where epsilon and epsilon(m) are sufficiently small positive numbers. Moreover, these solutions u(epsilon) -> 0 in H-1(R-N) as epsilon -> 0.
DOI10.1007/s00526-007-0091-z
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000247635600005
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/5189
Collection数学所
Corresponding AuthorLin, Fanghua
Affiliation1.NYU, Courant Inst Math Sci, New York, NY 10012 USA
2.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Ding, Yanheng,Lin, Fanghua. Solutions of perturbed Schrodinger equations with critical nonlinearity[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,2007,30(2):231-249.
APA Ding, Yanheng,&Lin, Fanghua.(2007).Solutions of perturbed Schrodinger equations with critical nonlinearity.CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,30(2),231-249.
MLA Ding, Yanheng,et al."Solutions of perturbed Schrodinger equations with critical nonlinearity".CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 30.2(2007):231-249.
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