- Turkish Journal of Mathematics
- Vol: 42 Issue: 2
- On a biharmonic equation involving slightly supercritical exponent
On a biharmonic equation involving slightly supercritical exponent
Authors : Kamal Ould Bouh
Pages : 487-501
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We consider the biharmonic equation with supercritical nonlinearity $ (P_\varepsilon ):$ $\Delta^{2} u = K|u|^{8/(n-4)+\varepsilon}u$ in $\Omega$, $\Delta u =u = 0$ on $\partial \Omega $, where $\Omega $ is a smooth bounded domain in $\mathbb{R}^n $, $n \geq 5 $, $K$ is a $C^3$ positive function, and $\varepsilon$ is a positive real parameter. In contrast with the subcritical case, we prove the nonexistence of sign-changing solutions of $ (P_\varepsilon )$ that blow up at two near points. We also show that $(P_\varepsilon)$ has no bubble-tower sign-changing solutions.Keywords : Sign-changing solutions, bubble-tower solution, fourth-order equation, supercritical exponent