Electron. J. Differential Equations, Vol. 2021 (2021), No. 03, pp. 1-17.

Existence and nonexistence for singular sublinear problems on exterior domains

Mageed Ali, Joseph A. Iaia

Abstract:
In this article we study the existence of radial solutions of $\Delta u + K(|x|)f(u)= 0$ on the exterior of the ball of radius R>0 centered at the origin in $\mathbb{R}^N$ with u=0 on $\partial B_{R}$, and $\lim_{|x| \to \infty} u(x)=0$ where N>2, $f(u) \sim \frac{-1}{|u|^{q-1}u} $ for u near 0 with 0<q<1, and $f(u) \sim |u|^{p-1}u$ for large |u| with 0<p<1. Also, $K(|x|) \sim |x|^{-\alpha}$ with $ N+q(N-2) < \alpha <2(N-1)$ for large |x|.

Submitted June 11, 2020. Published January 7, 2021.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domains; singular problem; sublinear; radial solution.
DOI: https://doi.org/10.58997/ejde.2021.03

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Mageed Ali
Department of Mathematics
University of North Texas, P.O. Box 311430
Denton, TX 76203-5017, USA
email: mageedali@my.unt.edu
Joseph A. Iaia
Department of Mathematics
University of North Texas, P.O. Box 311430
Denton, TX 76203-5017, USA
email: iaia@unt.edu

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