Electron. J. Differential Equations, Vol. 2017 (2017), No. 253, pp. 1-14.

Existence of solutions for sublinear equations on exterior domains

Joseph A. Iaia

In this article we prove the existence of an infinite number of radial solutions of $\Delta u + K(r)f(u)= 0$, one with exactly n zeros for each nonnegative integer n on the exterior of the ball of radius R>0, $B_{R}$, centered at the origin in ${\mathbb R}^{N}$ with u=0 on $\partial B_{R}$ and $\lim_{r \to \infty} u(r)=0$ where N>2, f is odd with f<0 on $(0, \beta) $, f>0 on $(\beta, \infty)$, $f(u)\sim u^p$ with 0<p<1 for large u and $K(r) \sim r^{-\alpha}$ with $0 < \alpha < 2$ for large r.

Submitted February 12, 2017. Published October 10, 2017.
Math Subject Classifications: 34B40, 35B05
Key Words: Exterior domains; semilinear; sublinear; radial.

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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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