Article
Existence and Bifurcation of the Positive Solutions for a Semilinear Equation with Critical Exponent
Journal of Differential Equations
(1996)
Abstract
In this paper, we consider the semilinear elliptic equation[formula]Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (∗)μpossesses at least one solution ifμ∈(0, μ*) and no solutions ifμ>μ*. Furthermore, (∗)μpossesses a unique solution whenμ=μ*, and at least two solutions whenμ∈(0, μ*) and 2<NN⩾6, under some monotonicity conditions onf((1.6)) we show that there exist two constants 0<μ**⩽μ**<μ* such that problem (∗)μpossesses a unique solution forμ∈(0, μ**), and at least two solutions ifμ∈(μ**, μ*).
Disciplines
Publication Date
September 1, 1996
Publisher Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Differential Equations. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Differential Equations, 130, 1, (September 1996) DOI# 10.1006/jdeq.1996.0138
Citation Information
Yinbin Deng and Yi Li. "Existence and Bifurcation of the Positive Solutions for a Semilinear Equation with Critical Exponent" Journal of Differential Equations Vol. 130 Iss. 1 (1996) Available at: http://works.bepress.com/yi_li/23/