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