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Existence of positive radial solutions for a superlinear semipositone p-Laplacian problem on the exterior of a ball

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  21 March 2018

Quinn Morris ,
Ratnasingham Shivaji  and
Inbo Sim
Quinn Morris
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Greensboro, 116 Petty Building, 317 College Avenue, Greensboro, NC 27402, USA (shivaji@uncg.edu)
Ratnasingham Shivaji
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Greensboro, 116 Petty Building, 317 College Avenue, Greensboro, NC 27402, USA (shivaji@uncg.edu)
Inbo Sim
Affiliation:
Department of Mathematics, University of Ulsan, Ulsan 680-749, Republic of Korea (ibsim@ulsan.ac.kr)
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Abstract

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We prove the existence of positive radial solutions to a class of semipositone p-Laplacian problems on the exterior of a ball subject to Dirichlet and nonlinear boundary conditions. Using variational methods we prove the existence of a solution, and then use a priori estimates to prove the positivity of the solution.

Keywords

semipositonep-Laplaciannonlinear boundary conditions

MSC classification

Secondary: 35J92: Quasilinear elliptic equations with $p$-Laplacian 35J20: Variational methods for second-order elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 2 , April 2018 , pp. 409 - 428
Copyright
Copyright © Royal Society of Edinburgh 2018