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Uniqueness of Positive Radial Solutions for a Class of Semipositone Systems on the Exterior of a Ball
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
Department of Mathematics and Physics, Faculty of Education, University of Gadarif, Gadarif, Sudan
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
Department of Science, College of Education, Sudan University of Science and Technology, Khartoum, Sudan
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 1 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 2 Department of Mathematics and Physics, Faculty of Education, University of Gadarif, Gadarif, Sudan
- 3 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 4 Department of Science, College of Education, Sudan University of Science and Technology, Khartoum, Sudan
- 5 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 6 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 7 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
Applied Mathematics·Volume 12 (2021)·Pages 131–146·Published 11 March 2021·DOI10.4236/am.2021.123009
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Abstract
In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP: , where Δ u = div ( ∇ u ) and Δ v = div ( ∇ v ) are the Laplacian of u , λ is a positive parameter, Ω = { x ∈ R n : N > 2, | x | > r 0 , r 0 > 0}, let i = [1,2] then K i :[ r 0 ,∞] → (0,∞) is a continuous function such that lim r →∞ k i ( r ) = 0 and is The external natural derivative, and : [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of f with a) f i > 0, b) f i < 0, and c) f i = 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings.
KeywordsElliptic SystemPositive Radial SolutionExterior DomainsFixed Point Index
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