A Critical Oscillation Constant as a Variable of Time Scales for Half-Linear Dynamic Equations
نویسنده
چکیده
We present criteria of Hille-Nehari type for the half-linear dynamic equation (r(t)Φ(y∆))∆+p(t)Φ(yσ) = 0 on time scales. As a particular important case we get that there is a a (sharp) critical constant which may be different from what is known from the continuous case, and its value depends on the graininess of a time scale and on the coefficient r. As applications we state criteria for strong (non)oscillation, examine generalized Euler type equations, and establish criteria of Kneser type. Examples from q-calculus and further possibilities for study are presented as well. Our results unify and extend many existing results from special cases, and are new even in the well-studied discrete case.
منابع مشابه
Dynamic Analysis of Moving Cables with Variable Tension and Variable Speed
Dynamic Analysis of an axially moving cable with time dependent tension and velocity isstudied in this paper. Tension force and the moving speed are assumed to be harmonic.It is found that there exists a specific value of speed in which natural frequency of the system approacheszero. This specific speed for such a critical condition is called critical speed and it will be proved thatincreasing ...
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 کاملFirst 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 کاملOscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales
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 th...
متن کاملTriple positive solutions of $m$-point boundary value problem on time scales with $p$-Laplacian
In this paper, we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian dynamic equation on time scales. We prove the existence at least three positive solutions of the boundary value problem by using the Avery and Peterson fixed point theorem. The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly. Our results ...
متن کامل