Existence and nonexistence of interior-peaked solution for a nonlinear Neumann problem

Daomin Cao, Ezzat S. Noussair, Shusen Yan

Type: Article

Publication Date: 2001-09-01

Citations: 24

DOI: https://doi.org/10.2140/pjm.2001.200.19

Abstract

We show that the critical problemhas no positive solutions concentrating, as λ → ∞, at interior points of Ω if a = 0, but for a class of symmetric domains Ω, the problem with a > 0 has solutions concentrating at interior points of Ω.

Locations

Pacific Journal of Mathematics - View - PDF

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+	Nonlinear Elliptic Equations Involving the Critical Sobolev Exponent—Survey and Perspectives	1987	H. Brézis
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+	Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents	1992	Wei-Ming Ni Xing‐Bin Pan Izumi Takagi
+	The role of the mean curvature in semilinear neumann problem involving critical exponent	1995	Adimurthi G.B. John Mancini S. L. Yadava
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+	On the diffusion coefficient of a semilinear Neumann problem	1988	Chang‐Shou Lin Wei‐Ming Ni
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+	Function Theory in the Unit Ball of ℂn	2012	Walter Rudin
+	Interaction between the Geometry of the Boundary and Positive Solutions of a Semilinear Neumann Problem with Critical Nonlinearity	1993	F. AdimurthiPacella S. L. Yadava