Affiliation:
1. School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China
2. Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Abstract
LetTbe a time scale anda,b∈T,a<ρ2(b). We study the nonlinear fourth-order eigenvalue problem onT,uΔ4(t)=λh(t)f(u(t),uΔ2(t)),t∈[a,ρ2(b)]T,u(a)=uΔ(σ(b))=uΔ2(a)=uΔ3(ρ(b))=0and obtain the existence and nonexistence of positive solutions when0<λ≤λ*andλ>λ*, respectively, for someλ*. The main tools to prove the existence results are the Schauder fixed point theorem and the upper and lower solution method.
Funder
China Postdoctoral Science Foundation
Subject
Applied Mathematics,Analysis
Cited by
1 articles.
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