We study the fourth-order nonlinear critical problem $\Delta^2 u = u^{2*−1}$ in a smooth, bounded domain $\Omega\subset R^n$, $n\geq 5$, subject to the boundary conditions $u = \Delta u − d u_{\nu}= 0$ on $\partial \Omega$. We provide estimates for the range of parameters $d\in R$ for which this problem admits a positive solution. If the domain is the unit ball, we obtain an almost complete description.

Critical growth biharmonic elliptic problems under Steklov-type boundary conditions / Berchio, Elvise; Gazzola, F.; Weth, T.. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - 12:(2007), pp. 381-406.

Critical growth biharmonic elliptic problems under Steklov-type boundary conditions

BERCHIO, ELVISE;
2007

Abstract

We study the fourth-order nonlinear critical problem $\Delta^2 u = u^{2*−1}$ in a smooth, bounded domain $\Omega\subset R^n$, $n\geq 5$, subject to the boundary conditions $u = \Delta u − d u_{\nu}= 0$ on $\partial \Omega$. We provide estimates for the range of parameters $d\in R$ for which this problem admits a positive solution. If the domain is the unit ball, we obtain an almost complete description.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2522496
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