Author(s)

Alhussein Mohamed^1*, Khalid Ahmed Abbakar^1,2, Abuzar Awad¹, Omer Khalil^1,3, Bechir Mahamat Acyl¹, Abdoulaye Ali Youssouf¹, Mohammed Mousa¹

¹College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.
²Department of Mathematics and Physics, Faculty of Education, University of Gadarif, Gadarif, Sudan.
³Department of Science, College of Education, Sudan University of Science and Technology, Khartoum, Sudan.

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 K_i :[r₀,∞] → (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.

Elliptic System, Positive Radial Solution, Exterior Domains, Fixed Point Index

Mohamed, A. , Abbakar, K. , Awad, A. , Khalil, O. , Acyl, B. , Youssouf, A. and Mousa, M. (2021) Uniqueness of Positive Radial Solutions for a Class of Semipositone Systems on the Exterior of a Ball. Applied Mathematics, 12, 131-146. doi: 10.4236/am.2021.123009.