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Positive Solutions to Semilinear Elliptic Equations with Logistic-Type Nonlinearities and Harvesting in Exterior Domains.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Positive Solutions to Semilinear Elliptic Equations with Logistic-Type Nonlinearities and Harvesting in Exterior Domains./
Author:	Jameson, Eric.
Description:	1 online resource (87 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-04, Section: B.
Contained By:	Dissertations Abstracts International84-04B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798845713155

Positive Solutions to Semilinear Elliptic Equations with Logistic-Type Nonlinearities and Harvesting in Exterior Domains.
Jameson, Eric.

Positive Solutions to Semilinear Elliptic Equations with Logistic-Type Nonlinearities and Harvesting in Exterior Domains. - 1 online resource (87 pages)

Source: Dissertations Abstracts International, Volume: 84-04, Section: B.

Thesis (Ph.D.)--University of Nevada, Las Vegas, 2022.

Includes bibliographical references

Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques for solving these equations in the whole space RN can be applied to the exterior domain with some modifications. Then, as a second approach, we use the Kelvin transform to move the equation inside the unit ball, solve it there, using the techniques for bounded domains, and then re-apply the Kelvin transform to obtain a solution to the original equation. We are then confronted with the natural question of whether the two different approaches provide a multiplicity result for positive solutions in our exterior domain. As part of this work we prove a uniqueness result under further assumptions on the data. Finally, we briefly show that the Kelvin transform method can also be applied to the case of N = 2 with some slight adjustments, and that the solution obtained in this case also satisfies a similar uniqueness property.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798845713155Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

AnalysisIndex Terms--Genre/Form:

554714
Electronic books.

Positive Solutions to Semilinear Elliptic Equations with Logistic-Type Nonlinearities and Harvesting in Exterior Domains.
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245 1 0 $a Positive Solutions to Semilinear Elliptic Equations with Logistic-Type Nonlinearities and Harvesting in Exterior Domains.
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500 $a Source: Dissertations Abstracts International, Volume: 84-04, Section: B.
500 $a Advisor: Tehrani, Hossein.
502 $a Thesis (Ph.D.)--University of Nevada, Las Vegas, 2022.
504 $a Includes bibliographical references
520 $a Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques for solving these equations in the whole space RN can be applied to the exterior domain with some modifications. Then, as a second approach, we use the Kelvin transform to move the equation inside the unit ball, solve it there, using the techniques for bounded domains, and then re-apply the Kelvin transform to obtain a solution to the original equation. We are then confronted with the natural question of whether the two different approaches provide a multiplicity result for positive solutions in our exterior domain. As part of this work we prove a uniqueness result under further assumptions on the data. Finally, we briefly show that the Kelvin transform method can also be applied to the case of N = 2 with some slight adjustments, and that the solution obtained in this case also satisfies a similar uniqueness property.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Applied mathematics. $3 1069907
653 $a Analysis
653 $a Calculus of variations
653 $a Differential equations
653 $a Mathematics
653 $a Nonlinear analysis
653 $a Partial differential equations
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710 2 $a University of Nevada, Las Vegas. $b Mathematical Sciences. $3 1474045
773 0 $t Dissertations Abstracts International $g 84-04B.
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