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), 874edfe89e5a4a8f8f619e47d760eb" title="Click to view the MathML source">1<p<n, λ is a positive parameter, 8841b469a4" title="Click to view the MathML source">r0>0 and 87c379d56a30bcd8320f8" title="Click to view the MathML source">ΩE:={x∈Rn | |x|>r0}. Here the weight function K∈C1[r0,∞) satisfies K(r)>0 for r≥r0, 873dce73529f" title="Click to view the MathML source">limr→∞K(r)=0, and the reaction term ae450" title="Click to view the MathML source">f∈C[0,∞)∩C1(0,∞) is strictly increasing and satisfies e9c4dae6a3f3497ab947229" title="Click to view the MathML source">f(0)<0 (semipositone), ae8bdbc77500934873d946bd58fe18">, lims→∞f(s)=∞, e95f6cd2"> and is nonincreasing on 9913f49afa626400eb66cbdec95e43bf" title="Click to view the MathML source">[a,∞) for some e9b" title="Click to view the MathML source">a>0 and 992323ff62a" title="Click to view the MathML source">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 884d51fa4f47191b7807ed63df861" title="Click to view the MathML source">λ≫1. We establish the uniqueness of this positive radial solution for 884d51fa4f47191b7807ed63df861" title="Click to view the MathML source">λ≫1.