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2007 Positive solutions of semilinear elliptic eigenvalue problems with concave nonlinearities
Kenichiro Umezu
Adv. Differential Equations 12(12): 1415-1436 (2007).

Abstract

In this paper, we prove the existence and nonexistence results for positive solutions to semilinear elliptic boundary value problems, with concave nonlinearities inside a smooth bounded domain and on the boundary. Our approach relies on sub and supersolutions, as well as the Nehari manifold that may contain the critical points for the energy functional associated with the boundary value problem. The fibering method helps us to study the properties of the Nehari manifold.

Citation

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Kenichiro Umezu. "Positive solutions of semilinear elliptic eigenvalue problems with concave nonlinearities." Adv. Differential Equations 12 (12) 1415 - 1436, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1180.35198
MathSciNet: MR2382731

Subjects:
Primary: 35J60
Secondary: 35J20, 35J25, 35J65, 47J30, 58E05

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 12 • 2007
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