Existence of Infinitely Many Solutions for Singular Semilinear Problems on Exterior Domains

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Article proving the existence of infinitely many radial solutions of โˆ†๐“Š+๐พ(๐“‡) ฦ’ (๐“Š) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in โ„แดบ with u = 0 on โˆ‚BR and lim/rโ†’โˆž ๐“Š(๐“‡) = 0 where N > 2, f is odd with f < 0 on (0, ฮฒ), f > 0 on (ฮฒ, โˆž), f is superlinear for large u, ฦ’(๐“Š) โˆผ โˆ’1/(|๐“Š|๐˜ฒโปยน๐“Š) with 0 < q < 1 for small u, and 0 < ๐พ(๐“‡) โ‰ค ๐พโ‚/rโˆ with ๐‘ + q(๐‘ โˆ’ 2) < โˆ < 2(๐‘โˆ’ 1) for โ€ฆ continued below

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Iaia, Joseph A. September 23, 2019.

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Article proving the existence of infinitely many radial solutions of โˆ†๐“Š+๐พ(๐“‡) ฦ’ (๐“Š) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in โ„แดบ with u = 0 on โˆ‚BR and lim/rโ†’โˆž ๐“Š(๐“‡) = 0 where N > 2, f is odd with f < 0 on (0, ฮฒ), f > 0 on (ฮฒ, โˆž), f is superlinear for large u, ฦ’(๐“Š) โˆผ โˆ’1/(|๐“Š|๐˜ฒโปยน๐“Š) with 0 < q < 1 for small u, and 0 < ๐พ(๐“‡) โ‰ค ๐พโ‚/rโˆ with ๐‘ + q(๐‘ โˆ’ 2) < โˆ < 2(๐‘โˆ’ 1) for large r.

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11 p.

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Abstract: In this article we prove the existence of infinitely many radial solutions of โˆ†๐“Š+๐พ(๐“‡) ฦ’ (๐“Š) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in โ„แดบ with u = 0 on โˆ‚BR and lim/rโ†’โˆž ๐“Š(๐“‡) = 0 where N > 2, f is odd with f < 0 on (0, ฮฒ), f > 0 on (ฮฒ, โˆž), f is superlinear for large u, ฦ’(๐“Š) โˆผ โˆ’1/(|๐“Š|๐˜ฒโปยน๐“Š) with 0 < q < 1 for small u, and 0 < ๐พ(๐“‡) โ‰ค ๐พโ‚/rโˆ with ๐‘ + q(๐‘ โˆ’ 2) < โˆ < 2(๐‘โˆ’ 1) for large r.

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  • Electron. J. Differential Equations, 2019(108), Texas State University, September 23, 2019, pp. 1-11

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  • Publication Title: Electronic Journal of Differential Equations
  • Volume: 2019
  • Issue: 108
  • Peer Reviewed: Yes

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  • March 9, 2018

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  • September 23, 2019

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  • June 15, 2022, 3:13 p.m.

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  • Nov. 28, 2023, 2:01 p.m.

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Iaia, Joseph A. Existence of Infinitely Many Solutions for Singular Semilinear Problems on Exterior Domains, article, September 23, 2019; (https://digital.library.unt.edu/ark:/67531/metadc1944180/: accessed January 14, 2025), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Science.

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