Existence of solutions for sublinear equations on exterior domains
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In 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 limr→∞ u(r) = 0 where N > 2, ƒ is odd with ƒ < 0 on (0, β), ƒ > 0 on (β, ∞), ƒ(u) ~ up 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 limr→∞ u(r) = 0.
CitationIaia, J. A. (2018). Existence of solutions for sublinear equations on exterior domains. Electronic Journal of Differential Equations, 2018(181), pp. 1-14.
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