Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-25T16:09:09.710Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)