Existence and nonexistence of solutions for sublinear equations on exterior domains

Date

2017-09-13

Authors

Iaia, Joseph

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article we study 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 where 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 2 < α < 2(N - 1) then there are no solutions with lim r→∞ u(r) = 0 for sufficiently large R > 0. On the other hand, if 2 < N - p(N - 2) < α < 2(N - 1) and k, n are nonnegative integers with 0 ≤ k ≤ n then there exist solutions, uk, with k zeros on (R, ∞) and limr→∞ uk(r) = 0 if R > 0 is sufficiently small.

Description

Keywords

Exterior domains, Semilinear, Sublinear, Radial

Citation

Iaia, J. A. (2017). Existence and nonexistence of solutions for sublinear equations on exterior domains. <i>Electronic Journal of Differential Equations, 2017</i>(214), pp. 1-13.

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Attribution 4.0 International

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