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 e6da6c268a9789e4eb4e64b8" title="Click to view the MathML source">Δpz:=div(|∇z|p−2∇z), 1<p<n, λ is a positive parameter, b469a4" title="Click to view the MathML source">r0>0 and ΩE:={x∈Rn | |x|>r0}. Here the weight function b30dd4c71b5b45379a0bfa1b2c54103e" title="Click to view the MathML source">K∈C1[r0,∞) satisfies K(r)>0 for b3b326cb2a7" title="Click to view the MathML source">r≥r0, limr→∞K(r)=0, and the reaction term f∈C[0,∞)∩C1(0,∞) is strictly increasing and satisfies e6a3f3497ab947229" title="Click to view the MathML source">f(0)<0 (semipositone), , a53bd48c510d1b7389e722600904" title="Click to view the MathML source">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 b42884d51fa4f47191b7807ed63df861" title="Click to view the MathML source">λ≫1. We establish the uniqueness of this positive radial solution for b42884d51fa4f47191b7807ed63df861" title="Click to view the MathML source">λ≫1.