Lyapunov-type Inequalities for Odd Order Linear Differential Equations
نویسندگان
چکیده
In this article, we obtain Lyapunov-type inequalities for certain odd order linear boundary-value problems. Our inequalities involve integrals of both q+(t) and q−(t) in addition to that of |q(t)|. The Green’s function for even order boundary-value problems plays a key role in our proofs. Also, using the Fredholm alternative theorem, we obtain a criterion for the existence and uniqueness of solutions to the corresponding nonhomogeneous linear boundaryvalue problems.
منابع مشابه
Lyapunov-type Inequalities for Third-order Linear Differential Equations
In this article, we establish new Lyapunov-type inequalities for third-order linear differential equations y′′′ + q(t)y = 0 under the three-point boundary conditions y(a) = y(b) = y(c) = 0 and y(a) = y′′(d) = y(b) = 0 by bounding Green’s functions G(t, s) corresponding to appropriate boundary conditions. Thus, we obtain the best constants of Lyapunov-type inequalities for three-point boundary v...
متن کاملLyapunov–type Inequalities for Third–order Linear Differential Equations
In this paper, we obtain new Lyapunov-type inequalities for the third-order linear differential equation x′′′ + q(t)x = 0 . Our work provides the sharpest results in the literature and makes corrections to those in a recently published paper [1]. Based on the above, we further establish new Lyapunov-type inequalities for more general third-order linear differential equations. Moreover, by combi...
متن کاملSome Lyapunov–type Inequalities for a Class of Nonlinear Systems
In this paper, we present some new Lyapunov-type inequalities for a class of nonlinear differential systems, which are natural generalizations of the well-known Lyapunov inequality for linear second order differential equations. The results of this paper generalize some previous results on this topic. Mathematics subject classification (2010): 34C11.
متن کاملRandom differential inequalities and comparison principles for nonlinear hybrid random differential equations
In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities have been proved for an IVP of first order hybrid random differential equations with the linear perturbation of second type. A comparison theorem is proved and applied to prove the uniqueness of random solution for the considered perturbed random differential eq...
متن کاملDynamic Systems and Applications 24 (2015) 211-220 LYAPUNOV TYPE INEQUALITIES FOR SECOND ORDER SUB AND SUPER-HALF-LINEAR DIFFERENTIAL EQUATIONS
In the case of oscillatory potential, we present a Lyapunov type inequality for second order differential equations of the form (r(t)Φβ(x ′(t)))′ + q(t)Φγ(x(t)) = 0, in the sub-half-linear (0 < γ < β) and the super-half-linear (0 < β < γ < 2β) cases where Φ∗(s) = |s|∗−1s. AMS (MOS) Subject Classification. 34C10, 34C15.
متن کامل