In this article we study radial solutions of on the exterior of the ball of radius R>0 centered at the origin in , where f is odd with f<0 on , f>0 on , for , and where the function K(r) is assumed to be positive and as . The primitive has a ``hilltop'' at . With mild assumptions on f we prove that if with then there are n solutions of on the exterior of the ball of radius R such that as if R>0 is sufficiently small. We also show there are no solutions if R>0 is sufficiently large.
Submitted January 6, 2020. Published December 1, 2020.
Math Subject Classifications: 34B40, 35B05.
Key Words: Sublinear equation; radial solution; exterior domain.
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| Joseph A. Iaia |
Department of Mathematics
University of North Texas, P.O. Box 311430
Denton, TX 76203-5017, USA
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