Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
842870 | Nonlinear Analysis: Theory, Methods & Applications | 2009 | 8 Pages |
Abstract
We consider existence of nonzero solutions to the following boundary value problem u″(t)+f(t,u)=0,t∈(0,1),u′(0)=αu(ξ),u′(1)+βu(η)=0, where αα and ββ are positive parameters, 0≤ξ<η≤10≤ξ<η≤1. We prove that solutions lose positivity as the parameter αα or ββ increases. In particular, we study problems where the associated integral equation has a kernel that changes sign. The proof is based on the fixed point theorem in cones.
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Authors
Hongxia Fan, Ruyun Ma,