A Generalized Wirtinger’s Inequality with Applications to a Class of Ordinary Differential Equations
نویسندگان
چکیده
We first prove a generalized Wirtinger’s inequality. Then, applying the inequality, we study estimates for lower bounds of periods of periodic solutions for a class of delay differential equations ẋ t −∑nk 1f x t − kr , and ẋ t − ∑n k 1g t, x t − ks , where x ∈ R, f ∈ C R,R , and g ∈ C R×Rp,Rp and r > 0, s > 0 are two given constants. Under some suitable conditions on f and g, lower bounds of periods of periodic solutions for the equations aforementioned are obtained.
منابع مشابه
Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes
Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...
متن کاملInterval Oscillation Criteria For A Class Of Nonlinear Fractional Differential Equations
In this work, some new interval oscillation criteria for solutions of a class of nonlinear fractional differential equations are established by using a generalized Riccati function and inequality technique. For illustrating the validity of the established results, we also present some applications for them. Key–Words: Oscillation; Interval criteria; Qualitative properties; Fractional differenti...
متن کاملReduction of Differential Equations by Lie Algebra of Symmetries
The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...
متن کاملSOLUTION OF FUZZY DIFFERENTIAL EQUATIONS UNDER GENERALIZED DIFFERENTIABILITY BY ADOMIAN DECOMPOSITION METHOD
Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the strongly generalized differentiability. Also one concrete application for ordinary fuzzy differential equation with fuzzy input data...
متن کاملThe Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear dierential equations with variable coecients
In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof th...
متن کامل