A note on a second order PDE with critical nonlinearity
In this work, we are interested in a nonlinear PDE of the form: $-\Delta u = K(x) u^\frac{n+2}{n-2}, u>0$ on $\Omega$ and $u=0$ on $\partial\Omega$, where $n\geq 3$ and $\Omega$ is a regular bounded domain of $\mathbb{R}^n$. Following the results of [K. Sharaf, Appl. Anal. 96(2017), No. 9, 146...
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| Format: | Article |
| Language: | English |
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University of Szeged
2019-02-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6737 |
| Summary: | In this work, we are interested in a nonlinear PDE of the form: $-\Delta u = K(x) u^\frac{n+2}{n-2}, u>0$ on $\Omega$ and $u=0$ on $\partial\Omega$, where $n\geq 3$ and $\Omega$ is a regular bounded domain of $\mathbb{R}^n$. Following the results of [K. Sharaf, Appl. Anal. 96(2017), No. 9, 1466−1482] and [K. Sharaf, On an elliptic boundary value problem with critical exponent, Turk. J. Math., to appear], we provide a full description of the loss of compactness of the problem and we establish a general index account formula of existence result, when the flatness order of the function $K$ at any of its critical points lies in $(1, \infty)$. |
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| ISSN: | 1417-3875 |