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The existence of a positive solution of semilinear elliptic equations with limiting Sobolev exponent

Published online by Cambridge University Press:  14 November 2011

Shixiao Wang
Shixiao Wang
Affiliation:
Department of Mathematics, Hill Center, Busch Campus, Rutgers University, New Brunswick, N.J. 08903, U.S.A
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Synopsis

Our paper concerns the existence of a positive solution for the equation:

A new condition, which guarantees the existence of a solution of the above equation, has been established. It has also given some sharp information in the cases where: (1) a(x) = λ = const. and Ω is a “thin” domain; (2) Ω is a ball and a(x) is a radially symmetrical function.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 117 , Issue 1-2 , 1991 , pp. 75 - 88
Copyright
Copyright © Royal Society of Edinburgh 1991

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