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Applications of opial and wirtinger inequalities on zeros of third order differential equations
Samir H. Saker,Saudi Arabia +1 more
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TLDR
In this paper, the authors established new inequalities of Lyapunov type for a third order differential equation, which give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zero derivatives.Abstract:
In this paper, for a third order differential equation, we will establish some new inequalities of Lyapunov type. These inequalities give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zeros of a solution and/or its derivatives. The main results will be proved by making use of the Holder inequality and some generalizations of Opial and Wirtinger type inequalities. Some examples are considered to illustrate the main results. AMS (MOS) Subject Classification. 34K11, 34C10read more
Citations
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Refinement multidimensional dynamic inequalities with general kernels and measures
TL;DR: In this paper, the properties of superquadratic and sub-squadratic functions are used to establish new refinement multidimensional dynamic inequalities of Hardy's type on time scales.
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Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales
TL;DR: In this paper, a new Opial dynamic inequalities involving higher order derivatives on time scales were proved by making use of Holder's inequality, a simple consequence of Keller's chain rule and Taylor monomials.
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Lyapunov's Type Inequalities for Fourth-Order Differential Equations
TL;DR: In this article, the authors established Lyapunov-type inequalities for a fourth-order differential equation, which gave lower bounds of the distance between zeros of a nontrivial solution and also lower bounds on the distances between zero derivatives of a solution and its derivatives.
Journal ArticleDOI
New gaps between zeros of fourth-order differential equations via Opial inequalities
TL;DR: In this paper, for a fourth-order differential equation, the authors established lower bounds for the distance between zeros of a nontrivial solution and their derivatives, and for the boundary value problems in the theory of bending of beams.
Journal ArticleDOI
Higher order dynamic inequalities on time scales
TL;DR: In this paper, the authors studied dynamic inequalities where the domain of the unknown function is a so-called time scale T, i.e., when T = R, T = N and T = q0 = {qt : t ∈ N0} where q > 1.
References
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Book
Opial Inequalities with Applications in Differential and Difference Equations
P.Y. Pang,Ravi P. Agarwal +1 more
TL;DR: In this paper, generalizations of Opial's Inequality are discussed, including Opial Inequalities Involving Higher Order Derivatives and Discrete Opial inequalities in Several Independent Variables.
Journal ArticleDOI
Lyapunov-type integral inequalities for certain higher order differential equations
TL;DR: First a short survey of the most basic results on Lyapunov inequality is given, and next this-type integral inequalities for certain higher order differential equations are obtained.
Journal ArticleDOI
On Liapunov-Type Inequality for Third-Order Differential Equations☆
N. Parhi,S. Panigrahi +1 more
TL;DR: In this article, a Liapunov-type inequality has been derived for a class of third-order differential equations of the form y + p t y = 0, wherepis a real-valued continuous function on [0, ∞] and the nature of the distance between consecutive two zeros or three zeros has been studied with the help of the inequality.
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On Liapunov-type inequality for certain higher-order differential equations
TL;DR: The well-known Liapunov-type inequality for a class of third-order differential equations without damping force to 2n+1 order differential equations is generalized.