Electron. J. Diff. Equ., Vol. 2016 (2016), No. 112, pp. 1-11.

Existence of solutions for semilinear problems with prescribed number of zeros on exterior domains

Janak Joshi, Joseph Iaia

Abstract:
In this article we prove the existence of an infinite number of radial solutions of $\Delta(u)+f(u)=0$ with prescribed number of zeros on the exterior of the ball of radius R>0 centered at the origin in ${\mathbb R}^{N}$ where f is odd with f<0 on $(0,\beta)$, f>0 on $(\beta,\infty)$ where $\beta>0$.

Submitted December 31, 2015. Published May 3, 2016.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domains; semilinear; superlinear; radial.

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Janak Joshi
Department of Mathematics
University of North Texas, P.O. Box 311430
Denton, TX 76203-1430, USA
email: janakrajjoshi@my.unt.edu
Joseph 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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