Nonexistence of positive solutions for some quasilinear elliptic equations in strip-like domains

Takahiro Hashimoto, Mitsuharu Otani

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    The nonexistence of positive solutions is discussed for -△pu = a(x)uq-1 in Ω, u|∂Ωn = 0, for the case where a(x) is a bounded positive function and Ω is a strip-like domain such as Ω = Ωd x ℝN-d with Ωd bounded in ℝd. The existence of nontrivial solution of (E) is proved by Schindler for q ∈ (p,p*) where p* is Sobolev's critical exponent. Our method of proofs for nonexistence rely on the "Pohozaev-type inequality" (for q ≥ p*); and on a new argument concerning the simplicity of the first eigenvalue for (generalized) eigenvalue problems combined with translation invariance of the domain (for q ≤ p).

    Original languageEnglish
    Pages (from-to)565-578
    Number of pages14
    JournalDiscrete and Continuous Dynamical Systems
    Volume3
    Issue number4
    Publication statusPublished - 1997

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics
    • Discrete Mathematics and Combinatorics

    Fingerprint Dive into the research topics of 'Nonexistence of positive solutions for some quasilinear elliptic equations in strip-like domains'. Together they form a unique fingerprint.

  • Cite this