Electron. J. Differential Equations, Vol. 2021 (2021), No. 68, pp. 1-17.

Infinitely many solutions for a singular semilinear problem on exterior domains

Mageed Ali, Joseph Iaia

In this article we prove the existence of an infinite number of radial solutions to Δ U + K(x)f(U)= 0 on the exterior of the ball of radius R>0 centered at the origin in RN 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 small $U \neq 0$ with 0<q<1, and $f(U) \sim |U|^{p-1}U$ for large |U| with p>1. Also, $K(x) \sim |x|^{-\alpha}$ with α>2(N-1) for large |x|.

Submitted November 2, 2020. Published August 10, 2021.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domain; semilinear equation; radial solution.

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Mageed Ali
Department of Mathematics
University of Kirkuk
Kirkuk, Iraq
email: mageedali@uokirkuk.edu.iq
Joseph Iaia
Department of Mathematics
University of North Texas
Denton, TX, USA
email: iaia@unt.edu

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