JournalspmVol. 70 , No. 1pp. 11–22

Another approach on an elliptic equation of Kirchhoff type

  • Anderson L.A. de Araujo

    Universidade Federal de Viçosa, Brazil
Another approach on an elliptic equation of Kirchhoff type cover
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Abstract

This paper is concerned with the existence of solutions to the class of nonlocal boundary value problems of the type

M(Ωu2)Δu=f(x,u), in Ω, u=0, on Ω,-M\left(\int_{\Omega}|\nabla u|^2\right)\Delta u = f(x,u), \text { in } \Omega, \ u=0, \text{ on } \partial \Omega,

where Ω\Omega is a smooth bounded domain of RN\mathbb{R}^N and MM is a positive continuous function. By assuming that f(x,u)f(x, u) is a Carathéodory function which growths at most uNN2|u|^{\frac{N}{N-2}}, N3N \geq 3, and under a suitable growth condition on MM, one proves an existence result by applying the Leray–Schauder fixed point theorem.

Cite this article

Anderson L.A. de Araujo, Another approach on an elliptic equation of Kirchhoff type. Port. Math. 70 (2013), no. 1 pp. 11–22

DOI 10.4171/PM/1923