Existence of Solutions for Sublinear Equations on Exterior Domains

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This article proves the existence of an infinite number of radial solutions of Δu+K(r)ƒ(u) = 0, one with exactly n zeros for each nonnegative integer n on the exterior of the ball of radius R > 0, Bʀ, centered at the origin in ℝᴺ with u = 0 on ∂Bʀ and limᵣ→∞u(r) = 0 where N > 2, f 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 0 < α < 2 for large r.

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14 p.

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Iaia, Joseph A. October 10, 2017.

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This article is part of the collection entitled: UNT Scholarly Works and was provided by the UNT College of Science to the UNT Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 25 times. More information about this article can be viewed below.

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This article proves the existence of an infinite number of radial solutions of Δu+K(r)ƒ(u) = 0, one with exactly n zeros for each nonnegative integer n on the exterior of the ball of radius R > 0, Bʀ, centered at the origin in ℝᴺ with u = 0 on ∂Bʀ and limᵣ→∞u(r) = 0 where N > 2, f 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 0 < α < 2 for large r.

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14 p.

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Abstract: In this article we prove the existence of an infinite number of radial solutions of Δu+K(r)ƒ(u) = 0, one with exactly n zeros for each nonnegative integer n on the exterior of the ball of radius R > 0, Bʀ, centered at the origin in ℝᴺ with u = 0 on ∂Bʀ and limᵣ→∞u(r) = 0 where N > 2, f 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 0 < α < 2 for large r.

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  • Electronic Journal of Differential Equations, 2017(253), Texas State University, October 10, 2017, pp. 1-14

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  • Publication Title: Electronic Journal of Differential Equations
  • Volume: 2017
  • Issue: 253
  • Peer Reviewed: Yes

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  • October 10, 2017

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  • July 5, 2018, 8:11 p.m.

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  • Nov. 28, 2023, 2:16 p.m.

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Iaia, Joseph A. Existence of Solutions for Sublinear Equations on Exterior Domains, article, October 10, 2017; San Marcos, Texas. (https://digital.library.unt.edu/ark:/67531/metadc1212065/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Science.

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