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| Problem with Critical Sobolev Exponent and with Weight |
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Citation： |
Rejeb HADIJI.Problem with Critical Sobolev Exponent and with Weight[J].Chinese Annals of Mathematics B,2007,28(3):327~352 |
| Page view： 1306
Net amount： 799 |
Authors： |
Rejeb HADIJI; |
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| Abstract： |
The authors consider the problem: $-{\rm div}(p\nabla u)={u}^{q
-{1}}+\lambda{u}$, $u > 0$ in $\Omega$, $u=0$ on $\partial
\Omega$, where $\Omega$ is a bounded domain in $\R^{n}$,
${n}\geq{3}$, $ p: \ov{\Omega}\rightarrow \R$ is a given positive
weight such that $p\in H^{1}(\Omega)\cap C(\ov{\Omega})$, $\lambda$ is a real constant and $q=\frac{2n}{n-2}$, and study
the effect of the behavior of $p$ near its minima and the impact of the geometry of domain on the existence of solutions for the above problem. |
Keywords： |
Critical Sobolev exponent, Variational methods |
Classification： |
35J20, 35J25, 35J60 |
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