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2012 Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales
Hua Luo, Chenghua Gao
Abstr. Appl. Anal. 2012(SI11): 1-17 (2012). DOI: 10.1155/2012/798796

Abstract

Let T be a time scale and a,bT, a<ρ2(b). We study the nonlinear fourth-order eigenvalue problem on T, uΔ4(t)=λh(t)f(u(t),uΔ2(t)), t[a,ρ2(b)]T, u(a)=uΔ(σ(b))=uΔ2(a)=uΔ3(ρ(b))=0 and obtain the existence and nonexistence of positive solutions when 0<λλ* and λ>λ*, respectively, for some λ*. The main tools to prove the existence results are the Schauder fixed point theorem and the upper and lower solution method.

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Hua Luo. Chenghua Gao. "Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales." Abstr. Appl. Anal. 2012 (SI11) 1 - 17, 2012. https://doi.org/10.1155/2012/798796

Information

Published: 2012
First available in Project Euclid: 4 April 2013

zbMATH: 1242.34157
MathSciNet: MR2926881
Digital Object Identifier: 10.1155/2012/798796

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI11 • 2012
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