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...

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Bibliographic Details
Main Author: Sharaf Khadijah
Format: Serial
Published: 2019
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Differenciálegyenlet - nemlineáris
doi:10.14232/ejqtde.2019.1.10

Online Access:http://acta.bibl.u-szeged.hu/58107
Description
Summary: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, ∞).
Physical Description:1-16
ISSN:1417-3875