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.
Highlights
We study the positive radial solutions for elliptic systems to the
We will first recall some important results from [8] where the authors studied the case of Dirichlet boundary condition, or equivalently (1.3) with the boundary condition t = 1 replaced by u= (1) v= (1) 0
These results do not depend on the boundary condition at t = 1 and it is true for solutions of (1.3)
Summary
We consider a steady state reaction diffusion equation on an exterior domain with a nonlinear boundary condition on the interior boundary. In [14], the authors study such a uniqueness result for the case of Dirichlet boundary condition on x = r0. We will first recall some important results from [8] where the authors studied the case of Dirichlet boundary condition, or equivalently (1.3) with the boundary condition t = 1 replaced by u= (1) v= (1) 0. These results do not depend on the boundary condition at t = 1 and it is true for solutions of (1.3).
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