Open Access
April, 2010 Degenerate elliptic boundary value problems with asymmetric nonlinearity
Kazuaki TAIRA
J. Math. Soc. Japan 62(2): 431-465 (April, 2010). DOI: 10.2969/jmsj/06220431


This paper is devoted to the study of a class of semilinear degenerate elliptic boundary value problems with asymmetric nonlinearity which include as particular cases the Dirichlet and Robin problems. The most essential point is how to generalize the classical variational approach to eigenvalue problems with an indefinite weight to the degenerate case. The variational approach here is based on the theory of fractional powers of analytic semigroups. By making use of global inversion theorems with singularities between Banach spaces, we prove very exact results on the number of solutions of our problem. The results extend an earlier theorem due to Ambrosetti and Prodi to the degenerate case.


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Kazuaki TAIRA. "Degenerate elliptic boundary value problems with asymmetric nonlinearity." J. Math. Soc. Japan 62 (2) 431 - 465, April, 2010.


Published: April, 2010
First available in Project Euclid: 7 May 2010

zbMATH: 1195.35158
MathSciNet: MR2662851
Digital Object Identifier: 10.2969/jmsj/06220431

Primary: 35J65
Secondary: 35J25 , 47H10

Keywords: degenerate boundary condition , fractional power , global inversion theorem with singularities , semilinear elliptic boundary value problem , variational method

Rights: Copyright © 2010 Mathematical Society of Japan

Vol.62 • No. 2 • April, 2010
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