Uniqueness of Positive Radial Solutions for a Class of Semipositone Systems on the Exterior of a Ball
Open Access
- 1 January 2021
- journal article
- research article
- Published by Scientific Research Publishing, Inc. in Applied Mathematics
- Vol. 12 (03), 131-146
- https://doi.org/10.4236/am.2021.123009
Abstract
In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP: , where Δu = div (∇u) and Δv = div (∇v) are the Laplacian of u, λ is a positive parameter, Ω = {x ∈ Rn : N > 2, |x| > r0, r0 > 0}, let i = [1,2] then Ki :[r0,∞] → (0,∞) is a continuous function such that limr→∞ ki(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) fi > 0, b) fi fi = 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings.Keywords
This publication has 15 references indexed in Scilit:
- Multiplicity results for classes of singular problems on an exterior domainDiscrete & Continuous Dynamical Systems, 2013
- Semipositone problems with falling zeros on exterior domainsJournal of Mathematical Analysis and Applications, 2013
- Uniqueness of nonnegative solutions for semipositone problems on exterior domainsJournal of Mathematical Analysis and Applications, 2012
- UNIQUENESS AND NONEXISTENCE OF POSITIVE SOLUTIONS TO SEMIPOSITONE PROBLEMSBulletin of the London Mathematical Society, 2006
- Positive solution curves of semipositone problems with concave nonlinearitiesProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1997
- Inequalities for second-order elliptic equations with applications to unbounded domains IDuke Mathematical Journal, 1996
- Uniqueness of non-negative solutions for a semipositone problem with concave nonlinearityCommunications in Partial Differential Equations, 1995
- Uniqueness and stability of nonnegative solutions for semipositone problems in a ballProceedings of the American Mathematical Society, 1993
- Nonnegative solutions for a class of radially symmetric nonpositone problemsProceedings of the American Mathematical Society, 1989
- On the Existence of Positive Solutions of Semilinear Elliptic EquationsSIAM Review, 1982