刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:1 January 2017
年:2017
卷:445
期:1
页码:459-475
全文大小:390 K
文摘
We consider steady state reaction diffusion equations on the exterior of a ball, namely, boundary value problems of the form:
where Δpz:=div(|∇z|p−2∇z), 1<p<n, λ is a positive parameter, r0>0 and ΩE:={x∈Rn | |x|>r0}. Here the weight function K∈C1[r0,∞) satisfies K(r)>0 for r≥r0, limr→∞K(r)=0, and the reaction term f∈C[0,∞)∩C1(0,∞) is strictly increasing and satisfies f(0)<0 (semipositone), , lims→∞f(s)=∞, and is nonincreasing on [a,∞) for some a>0 and q∈(0,p−1). For a class of such steady state equations it turns out that every nonnegative radial solution is strictly positive in the exterior of a ball, and exists for λ≫1. We establish the uniqueness of this positive radial solution for λ≫1.