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Positive solutions for non-homogeneous semilinear elliptic equations with data that changes sign

Published online by Cambridge University Press:  12 July 2007

Qiuyi Dai  and
Yonggeng Gu
Qiuyi Dai
Affiliation:
Department of Applied Mathematics, Hunan University, Changsha Hunan 410082, People's Republic of China
Yonggeng Gu
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha Hunan 410081, People's Republic of China
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Abstract

Let Ω ⊂ RN be a bounded domain. We consider the nonlinear problem and prove that the existence of positive solutions of the above nonlinear problem is closely related to the existence of non-negative solutions of the following linear problem: .

In particular, if p > (N + 2)/(N − 2), then the existence of positive solutions of nonlinear problem is equivalent to the existence of non-negative solutions of the linear problem (for more details, we refer to theorems 1.2 and 1.3 in § 1 of this paper).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 2 , April 2003 , pp. 297 - 306
Copyright
Copyright © Royal Society of Edinburgh 2003

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