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Multiple solutions of semilinear degenerate elliptic boundary value problems

✍ Scribed by Kazuaki Taira

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
177 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Dedicated to Professor Kyuya Masuda on the occasion of his 70th birthday

The purpose of this paper is to study a class of semilinear elliptic boundary value problems with degenerate boundary conditions which include as particular cases the Dirichlet problem and the Robin problem. The approach here is based on the super-sub-solution method in the degenerate case, and is distinguished by the extensive use of an L p Schauder theory elaborated for second-order, elliptic differential operators with discontinuous zero-th order term. By using Schauder's fixed point theorem, we prove that the existence of an ordered pair of sub-and supersolutions of our problem implies the existence of a solution of the problem. The results extend an earlier theorem due to Kazdan and Warner to the degenerate case.

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