Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Monotonicity of the forcing term and existence of positive solutions for a class of semilinear elliptic problems

Author: Gadam Sudhasree
Journal: Proc. Amer. Math. Soc. 113 (1991), 415-418
MSC: Primary 35B05; Secondary 35J65
MathSciNet review: 1059637
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the existence of positive solutions to the equation $ \Delta u + f(u) + \lambda g(\left\Vert x \right\Vert) = 0$ in the unit ball in $ {\mathbb{R}^N}$ with Dirichlet boundary conditions, where $ f$ is superlinear with $ f(0) = 0$ and $ \lambda $ is a real parameter. We prove that if $ g$ is monotonically increasing, then there exists an $ \alpha < 0$ such that for $ \lambda < \alpha $ the above equation has no positive solution. This is in contrast to the case of $ g$ monotonically decreasing, where positive solutions exist for all negative values of $ \lambda $.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35B05, 35J65

Retrieve articles in all journals with MSC: 35B05, 35J65

Additional Information

PII: S 0002-9939(1991)1059637-6
Article copyright: © Copyright 1991 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia