On multi-bump solutions of nonlinear Schrödinger equation with electromagnetic fields and critical nonlinearity in R N
In this paper, we study a class of nonlinear Schrödinger equations with electromagnetic fields and critical nonlinearity in RN:-ΔAu+(λV(x)+Z(x))u=βf(|u|2)u+|u|2∗-2u, where f is a continuous function, V,Z:RN→R are continuous functions verifying suitable hypotheses. We show that if the zero set of V(x...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2017-04, Vol.56 (2), p.1-29 |
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| creator | Liang, Sihua Shi, Shaoyun |
| description | In this paper, we study a class of nonlinear Schrödinger equations with electromagnetic fields and critical nonlinearity in RN:-ΔAu+(λV(x)+Z(x))u=βf(|u|2)u+|u|2∗-2u, where f is a continuous function, V,Z:RN→R are continuous functions verifying suitable hypotheses. We show that if the zero set of V(x) has several isolated connected components Ω1,…,Ωk such that the interior of Ωi is not empty and ∂Ωi is smooth, then for λ>0 large there exists, for any non-empty subset Γ⊂{1,…,k}, a bump solution trapped in a neighborhood of ∪j∈ΓΩj. |
| doi_str_mv | 10.1007/s00526-017-1116-x |
| format | Article |
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We show that if the zero set of V(x) has several isolated connected components Ω1,…,Ωk such that the interior of Ωi is not empty and ∂Ωi is smooth, then for λ>0 large there exists, for any non-empty subset Γ⊂{1,…,k}, a bump solution trapped in a neighborhood of ∪j∈ΓΩj.</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-017-1116-x</identifier><language>eng</language><publisher>Heidelberg: Springer Nature B.V</publisher><subject>Continuity (mathematics) ; Electromagnetic fields ; Electromagnetism ; Nonlinear equations ; Nonlinearity ; Schrodinger equation</subject><ispartof>Calculus of variations and partial differential equations, 2017-04, Vol.56 (2), p.1-29</ispartof><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Liang, Sihua</creatorcontrib><creatorcontrib>Shi, Shaoyun</creatorcontrib><title>On multi-bump solutions of nonlinear Schrödinger equation with electromagnetic fields and critical nonlinearity in R N</title><title>Calculus of variations and partial differential equations</title><description>In this paper, we study a class of nonlinear Schrödinger equations with electromagnetic fields and critical nonlinearity in RN:-ΔAu+(λV(x)+Z(x))u=βf(|u|2)u+|u|2∗-2u, where f is a continuous function, V,Z:RN→R are continuous functions verifying suitable hypotheses. 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| subjects | Continuity (mathematics) Electromagnetic fields Electromagnetism Nonlinear equations Nonlinearity Schrodinger equation |
| title | On multi-bump solutions of nonlinear Schrödinger equation with electromagnetic fields and critical nonlinearity in R N |
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