Asymptotic behavior of least energy solutions for a biharmonic problem with nearly critical growth

Article type: Research Article

Authors: Takahashi, Futoshi

Affiliations: Department of Mathematics, Graduate School of Science, Osaka City University, Sugimoto 3-3-138, Sumiyoshi-ku, Osaka, 558-8585, Japan. Tel.: +81 0 6-6605-2508, E-mail: [email protected]

Abstract: We study the asymptotic behavior of least energy solutions to the equation Δ2u=c0K(x)upε with the Navier boundary condition as ε→+0, where Ω is a smooth bounded domain in RN (N≥5), c0=(N−4)(N−2)N(N+2) and pε=(N+4)/(N−4)−ε, ε>0. Under some assumptions on the coefficient function K, we obtain fairly precise asymptotics of the L∞-norm of least energy solutions.

Keywords: biharmonic equation, critical exponent

DOI: 10.3233/ASY-2008-0904

Journal: Asymptotic Analysis, vol. 60, no. 3-4, pp. 213-226, 2008