A note on a second order PDE with critical nonlinearity
In this work, we are interested in a nonlinear PDE of the form: −∆u = K(x)u n+2 n−2 , u > 0 on Ω and u = 0 on ∂Ω, where n ≥ 3 and Ω is a regular bounded domain of Rn . Following the results of [K. Sharaf, Appl. Anal. 96(2017), No. 9, 1466– 1482] and [K. Sharaf, On an elliptic boundary value probl...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet - nemlineáris |
| doi: | 10.14232/ejqtde.2019.1.10 |
| Online Access: | http://acta.bibl.u-szeged.hu/58107 |
| Tartalmi kivonat: | In this work, we are interested in a nonlinear PDE of the form: −∆u = K(x)u n+2 n−2 , u > 0 on Ω and u = 0 on ∂Ω, where n ≥ 3 and Ω is a regular bounded domain of Rn . 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, ∞). |
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| Terjedelem/Fizikai jellemzők: | 1-16 |
| ISSN: | 1417-3875 |