A note on a mountain pass characterization of least energy solutions

Louis Jeanjean, Kazunaga Tanaka

    Research output: Contribution to journal › Article

    23 Citations (Scopus)

    Abstract

    We consider the equation -u" = g(u), u(x) ∈ H1(R). (0.1) Under general assumptions on the nonlinearity g we prove that the, unique up to translation, solution of (0.1) is at the mountain pass level of the associated functional. This result extends a corresponding result for least energy solutions when (0.1) is set on RN.

    Original languageEnglish
    Pages (from-to)445-455
    Number of pages11
    JournalAdvanced Nonlinear Studies
    Volume3
    Issue number4
    Publication statusPublished - 2003

    Fingerprint

    Least Energy Solutions
    Mountain Pass
    mountains
    nonlinearity
    Nonlinearity
    energy

    Keywords

    • Least energy solution
    • Mountain pass characterization

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematics(all)

    Cite this

    A note on a mountain pass characterization of least energy solutions. / Jeanjean, Louis; Tanaka, Kazunaga.

    In: Advanced Nonlinear Studies, Vol. 3, No. 4, 2003, p. 445-455.

    Research output: Contribution to journal › Article

    Jeanjean, L & Tanaka, K 2003, 'A note on a mountain pass characterization of least energy solutions', Advanced Nonlinear Studies, vol. 3, no. 4, pp. 445-455.
    Jeanjean L, Tanaka K. A note on a mountain pass characterization of least energy solutions. Advanced Nonlinear Studies. 2003;3(4):445-455.
    Jeanjean, Louis ; Tanaka, Kazunaga. / A note on a mountain pass characterization of least energy solutions. In: Advanced Nonlinear Studies. 2003 ; Vol. 3, No. 4. pp. 445-455.
    @article{fb7f084c6ffa4b638e4bd46346a4d1c0,
    title = "A note on a mountain pass characterization of least energy solutions",
    abstract = "We consider the equation -u{"} = g(u), u(x) ∈ H1(R). (0.1) Under general assumptions on the nonlinearity g we prove that the, unique up to translation, solution of (0.1) is at the mountain pass level of the associated functional. This result extends a corresponding result for least energy solutions when (0.1) is set on RN.",
    keywords = "Least energy solution, Mountain pass characterization",
    author = "Louis Jeanjean and Kazunaga Tanaka",
    year = "2003",
    language = "English",
    volume = "3",
    pages = "445--455",
    journal = "Advanced Nonlinear Studies",
    issn = "1536-1365",
    publisher = "Advanced Nonlinear Studies",
    number = "4",

    }

    TY - JOUR

    T1 - A note on a mountain pass characterization of least energy solutions

    AU - Jeanjean, Louis

    AU - Tanaka, Kazunaga

    PY - 2003

    Y1 - 2003

    N2 - We consider the equation -u" = g(u), u(x) ∈ H1(R). (0.1) Under general assumptions on the nonlinearity g we prove that the, unique up to translation, solution of (0.1) is at the mountain pass level of the associated functional. This result extends a corresponding result for least energy solutions when (0.1) is set on RN.

    AB - We consider the equation -u" = g(u), u(x) ∈ H1(R). (0.1) Under general assumptions on the nonlinearity g we prove that the, unique up to translation, solution of (0.1) is at the mountain pass level of the associated functional. This result extends a corresponding result for least energy solutions when (0.1) is set on RN.

    KW - Least energy solution

    KW - Mountain pass characterization

    UR - http://www.scopus.com/inward/record.url?scp=20144362610&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=20144362610&partnerID=8YFLogxK

    M3 - Article

    AN - SCOPUS:20144362610

    VL - 3

    SP - 445

    EP - 455

    JO - Advanced Nonlinear Studies

    JF - Advanced Nonlinear Studies

    SN - 1536-1365

    IS - 4

    ER -

    Access to Document