Oscillation criteria for a linear Riemann-Stieltjes integral equation system

Integral Criteria for Second-Order Linear Oscillation

We present several new criteria for the oscillation of the second-order linear equation y(t) + q(t)y(t) = 0, in which the coefficient q may or may not change signs. The criteria involve the integral ∫ tq(t) dt for some γ > 0. The special case γ = 2 is then studied in greater details. AMS Subject Classification: 34C10

A Companion of Ostrowski’s Inequality for the Riemann-stieltjes Integral

Interval Oscillation Criteria for Second-Order Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals

and Applied Analysis 3 where τ t and τj t are right-dense continuous functions satisfying limt→∞τ t limt→∞τj t ∞ for j 1, 2, . . . , n. Sun and Kong 14 studied the oscillation of the secondorder forced differential equation with the nonlinearity given by a Riemann-Stieltjes integral of the form ( p t x′ t )′ q t x t ∫b 0 r t, s φγ s x τ s dξ s e t , 1.6 where t ≥ 0, γ ∈ C 0, b is a strictly inc...

The Riemann-stieltjes Integral on Time Scales

We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given.

Integral averages and oscillation criteria for half-linear partial differential equation

The technique of weighted integral averages, known in the oscillation theory of ordinary differential equations, is extended to the half–linear partial differential equation div(||∇u||p−2∇u) + c(x)|u|p−2u = 0. p > 1 (E) This technique is used to obtain new oscillation criteria for (E) on the unbounded domains.