Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent

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Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent

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Publication Article, peer reviewed scientific
Title Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent
Author Cheng, Yuanji
Date 2006
English abstract
In this note we consider bifurcation of positive solutions to the semilinear elliptic boundary-value problem with critical Sobolev exponent -∆u = λu - αu^p+ u^{2^*-1}, u ≥ 0, in Ω u=0, on Ω. where Ω is a bounded C^2-domain in R^n, n ≥ 3, λ > λ_1, 1 < p < 2^* -1= (n+2)/(n-2) and α > 0 is a bifurcation parameter. Brezis and Nirenberg showed that a lower order (non-negative) perturbation can contribute to regain the compactness and whence yields existence of solutions. We study the equation with an indefinite perturbation and prove a bifurcation result of two solutions for this equation.
Link http://ejde.math.txstate.edu/Volumes/2006/135/cheng.pdf (external link to publication)
Publisher Department of Mathematics Texas State University-San Marcos, USA
Host/Issue Electronic Journal of Differential Equations,
Volume 2006
ISSN 1072-6691
Pages article 135, 1-8
Language eng (iso)
Subject Critical exponent
Bifurcation
Indefinite peturbation
Brezis- Nirenberg problem
Sciences
Research Subject Categories::MATHEMATICS
Handle http://hdl.handle.net/2043/10621 Permalink to this page
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