Turkish Journal of Mathematics
DOI
10.3906/mat-1611-57
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
First Page
487
Last Page
501
Recommended Citation
BOUH, KAMAL OULD
(2018)
"On a biharmonic equation involving slightly supercritical exponent,"
Turkish Journal of Mathematics: Vol. 42:
No.
2, Article 6.
https://doi.org/10.3906/mat-1611-57
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss2/6
