Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales
نویسندگان
چکیده
This paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation r t xΔ t γ Δ p t x g t 0 on an arbitrary time scale T with sup T ∞, where g t ≥ t and ∫∞ to Δs/ r1/γ s < ∞. Some sufficient conditions for oscillation of the studied equation are established. Our results not only improve and complement those results in the literature but also unify the oscillation of the second-order half-linear advanced differential equation and the second-order half-linear advanced difference equation. Three examples are included to illustrate the main results.
منابع مشابه
First order linear fuzzy dynamic equations on time scales
In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.
متن کاملNew comparison and oscillation theorems for second-order half-linear dynamic equations on time scales
∧ second-order half-linear dynamic equation (r(t)(x(t))) + p(t)x(σ (t)) = 0, where r(t) > 0, p(t) are continuous, ∫ ∞ t0 (r(t)) 1 α ∆t = ∞, α is a quotient of odd positive integers. In particular, no explicit sign assumptions aremadewith respect to the coefficient p(t). We give conditions under which every positive solution of the equations is strictly increasing. For α = 1, T = R, the result i...
متن کاملOn the Oscillation of Second-Order Nonlinear Neutral Delay Dynamic Equations on Time Scales
Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation ...
متن کاملHalf-Linear Dynamic Equations
Abstract. We survey half-linear dynamic equations on time scales. These contain the well-known half-linear differential and half-linear difference equations as special cases, but also other kinds of half-linear equations. Special cases of half-linear equations are the well-studied linear equations of second order. We discuss existence and uniqueness of solutions of corresponding initial value p...
متن کاملOscillation theorems for second-order nonlinear neutral dynamic equations with variable delays and damping
In this paper, we study the oscillation of a class of second-order nonlinear neutral damped variable delay dynamic equations on time scales. By using a generalized Riccati transformation technique, we obtain some sufficient conditions for the oscillation of the equations. The results of this paper improve and extend some known results. We also illustrate our main results with some examples. Key...
متن کامل