A note on a second order PDE with critical nonlinearity

Sharaf, Khadijah: A note on a second order PDE with critical nonlinearity. Electronic journal of qualitative theory of differential equations 10. pp. 1-16. (2019)

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Abstract

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, ∞).

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 10
Page Range: pp. 1-16
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.10
Uncontrolled Keywords: Differenciálegyenlet - nemlineáris
Additional Information: Bibliogr.: p. 14-16. ; összefoglalás angol nyelven
Date Deposited: 2019. May. 31. 06:30
Last Modified: 2019. May. 31. 06:30
URI: http://acta.bibl.u-szeged.hu/id/eprint/58107

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