Uniqueness of Positive Radial Solutions for a Class of Semipositone Systems on the Exterior of a Ball

• 作者: Alhussein Mohamed Khalid Ahmed Abbakar Abuzar Awad Omer Khalil Bechir Mahamat Acyl Abdoulaye Ali Youssouf Mohammed Mousa
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Elliptic System Positive Radial Solution Exterior Domains Fixed Point Index
• 年，卷（期）: 2021,（3）
• 页码范围: 131-146
• 页数: 16页
• 分类号: O17

摘要

In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP:<br /> <p> <img src="Edit_4da56369-d8f9-42d0-9650-c15af375d30c.bmp" alt="" />, where Δ<em>u</em> = <em>div</em> (<span style="white-space:nowrap;">&#8711;</span><em>u</em>) and Δ<em>v</em> = <em>div</em> (<span style="white-space:nowrap;">&#8711;</span><em>v</em>) are the Laplacian of <em>u</em>, <span style="white-space:nowrap;"><em>&#955;</em> </span>is a positive parameter, Ω = {<em>x</em> ∈ R^<em>n</em> : <em>N</em> > 2, |<em>x</em>| > <em>r</em>₀, <em>r</em>₀ > 0}, let <em>i</em> = [1,2] then <em>K_i</em> :[<em>r</em>₀,∞] → (0,∞) is a continuous function such that lim_{<em>r</em>→∞} <em>k_i</em>(<em>r</em>) = 0 and <img src="Edit_19f045da-988f-43e9-b1bc-6517f5734f9c.bmp" alt="" /> is The external natural derivative, and <img src="Edit_3b36ed6b-e780-46de-925e-e3cf7c6a125f.bmp" alt="" />: [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of <em>f </em>with a) <em>f_i</em>> 0, b) <em>f_i</em>< 0, and c) <em>f_i</em>= 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings. </p>