Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Monotonicity of the forcing term and existence of positive solutions for a class of semilinear elliptic problems
HTML articles powered by AMS MathViewer

by Gadam Sudhasree PDF
Proc. Amer. Math. Soc. 113 (1991), 415-418 Request permission

Abstract:

We study the existence of positive solutions to the equation $\Delta u + f(u) + \lambda g(\left \| x \right \|) = 0$ 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
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
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 415-418
  • MSC: Primary 35B05; Secondary 35J65
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1059637-6
  • MathSciNet review: 1059637