Affiliation:
1. Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
2. Centre of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand
Abstract
By using Krasnoselskii's fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problemΔ2u(t-1)+a(t)f(u(t))=0,t∈{1,2,…,T},u(0)=β∑s=1ηu(s),u(T+1)=α∑s=1ηu(s), wherefis continuous,T≥3is a fixed positive integer,η∈{1,2,...,T-1},0<α<(2T+2)/η(η+1),0<β<(2T+2-αη(η+1))/η(2T-η+1),andΔu(t-1)=u(t)-u(t-1). We show the existence of at least one positive solution iffis either superlinear or sublinear.
Funder
Commission on Higher Education, Thailand
Cited by
1 articles.
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