Electron. J. Differential Equations, Vol. 2020 (2020), No. 34, pp. 1-10.

Existence of solutions for semilinear problems on exterior domains

Joseph Iaia

In this article we prove the existence of an infinite number of radial solutions to $\Delta u+K(r)f(u)=0$ on $\mathbb{R}^{N}$ such that $\lim_{r \to \infty} u(r)=0$ with prescribed number of zeros on the exterior of the ball of radius R>0 where f is odd with f<0 on $(0,\beta)$, f>0 on $(\beta,\infty)$ with f superlinear for large $u$, and $K(r) \sim r^{-\alpha}$ with $ \alpha > 2(N-1)$.

Submitted January 12, 2019. Published April 15, 2020.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domain; superlinear; radial solution.

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Joseph A. Iaia
Department of Mathematics
University of North Texas, P.O. Box 311430
Denton, TX 76203-1430, USA
email: iaia@unt.edu

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