Differential and Integral Equations

On a Paneitz-type equation in six-dimensional domains

Hichem Chtioui and Khalil El Mehdi

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In this paper, we consider the equation $\Delta ^2 u=K u^5$, $u>0$ in $\Omega$, $u=\Delta u=0$ on $\partial\Omega$, where $K$ is a positive function and $\Omega$ is a bounded and smooth domain in $\mathbb R^6$. Using the theory of critical points at infinity, we give some topological conditions on $K$ to ensure some existence results.

Article information

Differential Integral Equations, Volume 17, Number 5-6 (2004), 681-696.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J40: Boundary value problems for higher-order elliptic equations
Secondary: 35J60: Nonlinear elliptic equations 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)


Chtioui, Hichem; El Mehdi, Khalil. On a Paneitz-type equation in six-dimensional domains. Differential Integral Equations 17 (2004), no. 5-6, 681--696. https://projecteuclid.org/euclid.die/1356060355

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