Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
841287 | Nonlinear Analysis: Theory, Methods & Applications | 2009 | 9 Pages |
Abstract
In this paper, we consider the following multipoint boundary value problem with one-dimensional ϕϕ-Laplacian (ϕ(x′(t)))′+q(t)f(t,x(t),x′(t))=0,t∈(0,1),x(0)=∑i=1n−2αix(ξi),ϕ(x′(1))=∑i=1n−2βiϕ(x′(ξi)), where ϕ(⋅)ϕ(⋅) is an odd and increasing homeomorphism, ξi∈(0,1)ξi∈(0,1) with 0<ξ1<ξ2<⋯<ξn−2<10<ξ1<ξ2<⋯<ξn−2<1, αiαi and βiβi are nonnegative constants and f(t,x(t),x′(t))f(t,x(t),x′(t)) is continuous and allowed to change sign. By fixed point theorems, we obtain new results on the existence of at least three positive solutions of this boundary value problem, which includes and improves some related results in the relevant literature.
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Authors
Yu Yang, Dongmei Xiao,