Exact multiplicity of positive solutions for a p-Laplacian equation with positive convex nonlinearity

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• 作者：Yulian An^a ; Chan-Gyun Kim^b ; Junping Shi^c ; ^{jxshix@wm.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J05 ; 35J25 ; 35B32 ; 34B18
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 February 2016
• 年：2016
• 卷：260
• 期：3
• 页码：2091-2118
• 全文大小：450 K

文摘

A p-Laplacian nonlinear elliptic equation with positive and p  -superlinear nonlinearity and Dirichlet boundary condition is considered. We first prove the existence of two positive solutions when the spatial domain is symmetric or strictly convex by using a priori estimates and topological degree theory. For the ball domain in R^N${\mathbb{R}}^N$ with N≥4$N\ge 4$ and the case that 1<p<2$1<p<2$, we prove that the equation has exactly two positive solutions when a parameter is less than a critical value. Bifurcation theory and linearization techniques are used in the proof of the second result.