Electron. J. Differential Equations, Vol. 2019 (2019), No. 108, pp. 1-11.

Existence of infinitely many solutions for singular semilinear problems on exterior domains

Joseph A. Iaia

In this article we prove the existence of infinitely many radial solutions of $\Delta u + K(r)f(u)= 0$ 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 is superlinear for large u, $f(u) \sim-1/(|u|^{q-1}u)$ with 0<q<1 for small u, and $0< K(r) \leq K_1/r^{\alpha}$ with $N+q(N-2) < \alpha< 2(N-1) $ for large r.

Submitted March 9, 2018. Published September 23, 2019.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domain; semilinear; singular; superlinear; radial solution.

Show me the PDF file (335 KB), TEX file for this article.

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

Return to the EJDE web page