Abstract
In this paper, we establish some interval oscillation criteria for a class of second-order nonlinear forced differential equations with variable exponent growth conditions. Our results not only give the sufficient conditions for the oscillation of equations with variable exponent growth conditions, but also they extend some existing results in the literature for equations with a Riemann-Stieltjes integral. Two examples are also considered to illustrate the main results.
Highlights
Which have been observed in Sun and Kong [ ]
2 Main results In the sequel, we denote by Lξ [a, b] the set of Riemann-Stieltjes integrable functions on [a, b] with respect to ξ
Where Q(t) is defined by ( ) with θ (t) ≡ β(t). Multiplying both sides of ( ) by v (t), integrating every term from a to b, and using integration by parts, we find b
Summary
Introduction In this paper, we will establish some interval oscillation criteria for the following equation: b p(t)u (t) + q(t)u(t) + g(t, s) u(t) γ (t,s)+ –β(t) sgn u(t) dξ (s) = e(t), t ≥ t , ( ) For the particular case when γ (t, s) = α(s), a = , and β(t) ≡ , equation ( ) reduces to the following equation: b p(t)u (t) + q(t)u(t) + g(t, s) u(t) α(s) sgn u(t) dξ (s) = e(t), ( )
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