higher order Lyapunov equations
An improvement of the Lyapunov inequality for certain higher order differential equations
... then, Lyapunov inequality and many of its generalizations have gained a great deal of attention (see [3–12] and the references therein), because these results have found many applications in the study of various ...
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Lyapunov type inequalities for certain higher order difference equations with mixed non linearities
... the Lyapunov-type inequality and many of its generalizations due to its broad applications in the study of various properties of solu- tions of differential and difference equations such as oscillation ...
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Lyapunov type inequalities for 2M th order equations under clamped free boundary conditions
... Later, Das and Vatsala [] gave the proof and extended the result by constructing the Green function. Other interesting developments for higher-order equations are seen in [–]. For example, as ...
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A generalized Lyapunov inequality for a higher order fractional boundary value problem
... the Lyapunov inequality. The Lyapunov inequality proved to be very useful in various problems related with differential ...about Lyapunov inequality were ...
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Lyapunov type inequalities for even order differential equations with mixed nonlinearities
... The Lyapunov inequality and its generalizations have been used successfully in connec- tion with oscillation and Sturmian theory, asymptotic theory, disconjugacy, eigenvalue problems, and various properties of the ...
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Lyapunov type inequalities for a class of even order differential equations
... where a, b Î ℝ with a <b, and the constant 4 cannot be replaced by a larger num- ber, where and in the sequel q + (t) = max{q(t), 0}. Since then, there are many improve- ments and generalizations of (1.2) in some ...
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Existence and Lyapunov Stability of Periodic Solutions for Generalized Higher-Order Neutral Differential Equations
... differential equations, and then by applying Mawhin’s continuation theory and some new inequalities, we obtain sufficient conditions for the existence of periodic solutions for ...The Lyapunov stability of ...
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On multivariate higher order Lyapunov type inequalities
... new Lyapunov-type inequalities for a class of even-order partial differential equations; the results of this paper are new which generalize and improve some early results in the ...
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On Lyapunov type inequalities for fourth order linear differential equations
... Recently, Lyapunov-type inequalities have been obtained for higher order linear di¤erential equations which satisfy n-point boundary conditions, but as far as we know, there are fewer studies ...
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Lyapunov type inequalities for the Riemann Liouville fractional differential equations of higher order
... We conclude this paper with the following remarks. The results obtained in this paper for equation (.) under the boundary conditions (.) or (.) can be easily generalized to the Riemann-Liouville fractional ...
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Asymptotic Expansions for Higher Order Scalar Difference Equations
... where y is a nontrivial characteristic solution of (2.3) corresponding to the set Λ (μ). As a preparation for the proof of Theorem 2.3, we establish a useful technical result. Recall that if g is a meromorphic function ...
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Oscillation for higher order differential equations with a middle term
... has been considered. In [] sufficient conditions are obtained for the existence of solu- tions, which are equivalent to a polynomial. In [] a criterion is given for existence of nonoscillatory solutions with non-zero ...
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On Periodic Solutions of Higher-Order Functional Differential Equations
... 17 S. R. Baslandze and I. Kiguradze, “On the unique solvability of a periodic boundary value problem for third-order linear differential equations,” Differentsial’nye Uravneniya, vol. 42, no. 2, pp. 153–158, ...
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Oscillation of higher order differential equations with distributed delay
... In this paper, by employing a refinement of the generalized Riccatti transformations and new comparison principles we have established new oscillation criteria for higher-order nonlinear differential ...
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Qualitative behavior of rational difference equations of higher order
... [13] E. A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, Chapman & Hall/CRC, 2005. [14] E. A. Grove, C. M. Kent, G. Ladas, R. Levins, and S. Valicenti, Global stability in some ...
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Periodic solutions for a class of higher order difference equations
... Difference equations have attracted the interest of many researchers in the last 20 years since they provided a natural description of several discrete models, in which the periodic solution problem is always a ...
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Solution of polynomial Lyapunov and Sylvester equations
... This chapter is organized as follows. In Section 2 we review several concepts from the literature regarding polynomial matrices and shifts in a single variable. In Section 3 these notions are extended to the case of ...
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On hyper order of solutions of higher order linear differential equations with meromorphic coefficients
... differential equations. For an introduction to the theory of differential equations in the complex plane by using Nevanlinna theory; see, for example ...The order of growth of solutions of the ...
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NEW ITERATIVE METHOD FOR SOLVING HIGHER ORDER KDV EQUATIONS
... 301 | P a g e solutions for the seventh order. Graphical representations of NIM solutions and exact solutions for Lax equations of fifth and seventh order are shown in Figures 1 and 3 respectively. ...
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On the oscillation of higher order nonlinear neutral difference equations
... difference equations has been stud- ied vigorously, for example, see [1–26] and the references cited ...difference equations find various applications in some variational problems, in natural science and ...
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