MR2976042 N. AZZOUZ and A. BENSEDIK N. AZZOUZ and A. BENSEDIK Funkcialaj Ekvacioj. Serio Internacia 55 2012 55--66 http://fe.math.kobe-u.ac.jp/FE/FullPapers/55-1/55_55.pdf http://www.ams.org/mathscinet-getitem?mr=MR2976042 Let $\Omega$ be a bounded domain in $\R^N$ $(N>2)$. We are concerned with the existence and nonexistence of solutions for the following nonlocal problem, $-M(\int_{\Omega}|\nabla u(x)|^{2}\,dx)\Delta u=|u|^{p-1}u+\lambda f(x)$ in $\Omega$, $u_{|_{\partial\Omega}}=0$. Where $M$ is continuous function on $\R^+$ and $f\in C^1(\overline{\Omega})$ changes sign. $\lambda$ and $p$ are positive parameters. By direct variational method, Galerkin approach and sub and super solutions method some results are established. Equation of Kirchhoff-type, Galerkin method, Sub and super solutions, Critical point. 35A15, 35A16, 35J25. 55-55 2012 N. AZZOUZ and A. BENSEDIK N. AZZOUZ and A. BENSEDIK

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