Abstract and Applied Analysis

Oscillation Criteria for Functional Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integral

Yuangong Sun and Taher S. Hassan

Full-text: Open access

Abstract

We present new oscillation criteria for the second order nonlinear dynamic equation [ r ( t ) ϕ γ ( x Δ ( t ) ) ] Δ + q 0 ( t ) ϕ γ ( x ( g 0 ( t ) ) ) + a b q ( t , s ) ϕ α ( s ) ( x ( g ( t , s ) ) ) Δ ζ ( s ) = 0 under mild assumptions. Our results generalize and improve some known results for oscillation of second order nonlinear dynamic equations. Several examples are worked out to illustrate the main results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 697526, 9 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425049097

Digital Object Identifier
doi:10.1155/2014/697526

Mathematical Reviews number (MathSciNet)
MR3200801

Zentralblatt MATH identifier
07022902

Citation

Sun, Yuangong; Hassan, Taher S. Oscillation Criteria for Functional Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integral. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 697526, 9 pages. doi:10.1155/2014/697526. https://projecteuclid.org/euclid.aaa/1425049097


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