Iaia, Joseph2022-03-102022-03-102018-11-06Iaia, J. A. (2018). Existence of solutions for sublinear equations on exterior domains. <i>Electronic Journal of Differential Equations, 2018</i>(181), pp. 1-14.1072-6691https://hdl.handle.net/10877/15477In this article we consider the radial solutions of ∆u + K(r)ƒ(u) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in ℝN with u = 0 on ∂BR and lim r→∞ u(r) = 0 where N > 2, ƒ is odd with ƒ < 0 on (0, β), ƒ > 0 on (β, ∞), ƒ(u) ~ u p with 0 < p < 1 for large u and K(r) ~ r-α with (N+2)-p(N-2)/2 ≤ α < N - p(N - 2) for large r. We prove existence of n solutions - one with exactly n zeros on [R, ∞) - if R > 0 is sufficiently small. If R > 0 is sufficiently large then there are no solutions with lim r→∞ u(r) = 0.Text14 pages1 file (.pdf)enAttribution 4.0 InternationalExterior domainsSemilinearSublinearRadial solutionArticle