Abstract and Applied Analysis

Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales

Hua Luo and Chenghua Gao

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Abstract

Let T be a time scale and a , b T , a < ρ 2 ( b ) . We study the nonlinear fourth-order eigenvalue problem on T , u Δ 4 ( t ) = λ h ( t ) f ( u ( t ) , u Δ 2 ( t ) ) , t [ a , ρ 2 ( b ) ] T , u ( a ) = u Δ ( σ ( b ) ) = u Δ 2 ( a ) = u Δ 3 ( ρ ( b ) ) = 0 and obtain the existence and nonexistence of positive solutions when 0 < λ λ * 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.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 798796, 17 pages.

Dates
First available in Project Euclid: 4 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365099944

Digital Object Identifier
doi:10.1155/2012/798796

Mathematical Reviews number (MathSciNet)
MR2926881

Zentralblatt MATH identifier
1242.34157

Citation

Luo, Hua; Gao, Chenghua. Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 798796, 17 pages. doi:10.1155/2012/798796. https://projecteuclid.org/euclid.aaa/1365099944


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