Lossy transmision lines terminated by -loads with exponential V–I characteristics

Angelov, Vasil G.

doi:10.1016/j.nonrwa.2006.01.002

Cited by 6 publications

(1 citation statement)

References 12 publications

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“…Example 6 (Lopes et al [8,9,13,15,23]). Consider the NFDE (2) which arises from a transmission line model, where > 0, > 0, > 0, | | < 1, ∈ (R), and is a given nonlinear function.…”

Section: Examplesmentioning

confidence: 99%

On the Existence and Stability of Periodic Solutions for a Nonlinear Neutral Functional Differential Equation

Yuan

Guo

2013

Abstract and Applied Analysis

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This paper deals with the existence and stability of periodic solutions for the following nonlinear neutral functional differential equation(d/dt)Dut=p(t)-au(t)-aqu(t-r)-h(u(t),u(t-r)).By using Schauder-fixed-point theorem and Krasnoselskii-fixed-point theorem, some sufficient conditions are obtained for the existence of asymptotic periodic solutions. Main results in this paper extend the related results due to Ding (2010) and Lopes (1976).

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“…Example 6 (Lopes et al [8,9,13,15,23]). Consider the NFDE (2) which arises from a transmission line model, where > 0, > 0, > 0, | | < 1, ∈ (R), and is a given nonlinear function.…”

Section: Examplesmentioning

confidence: 99%

On the Existence and Stability of Periodic Solutions for a Nonlinear Neutral Functional Differential Equation

Yuan

Guo

2013

Abstract and Applied Analysis

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Periodicity and stability in neutral equations by Krasnoselskii’s fixed point theorem

Ding

2010

Nonlinear Analysis: Real World Applications

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Recent Advances in Oscillation Theory 2011

Rogovchenko

Berezansky²,

Braverman³

et al. 2011

International Journal of Differential Equations

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Theory of oscillations is an important and well-established branch of the modern theory of differential equations concerned, in a broad sense, with the study of oscillatory phenomena arising in applied problems in technology, natural, and social sciences. Theoretical aspects of the classical theory of oscillations regard existence and nonexistence of oscillatory periodic, almost periodic, etc. solutions to a given equation or system, and description of asymptotic behavior of such solutions. It is well known that oscillation of solutions is an intrinsic feature of many dynamical systems. Furthermore, oscillations can be induced in a nonoscillatory system by nonlinear terms, delayed or advanced arguments, randomness, though these factors may also destroy oscillations arising in the original system.Papers included in this special issue address a number of challenging problems related to nonlinear oscillations, and describe novel techniques and approaches to classical problems in the theory of oscillations and beyond. Although the main focus of this issue is on oscillations, the editors are pleased to acknowledge several interesting contributions that develop new general methods applicable to wide classes of problems and deal with questions that are not directly related to oscillations.The issue opens with the contribution by H. A. Agwo et al. who use a generalized Riccati transformation, monotonicity arguments, and standard results on dynamic equations for establishing oscillation criteria for a class of second-order nonlinear delay dynamic equations on time scales. Several examples illustrate theoretical results.V. G. Angelov and D. Tz. Angelova study a lossless transmission line terminated by a nonlinear resistive load and parallel connected capacitance. Using Krasnoselskii fixed point theorem, they establish existence of solutions to an equivalent initial value problem for

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Lossy transmision lines terminated by -loads with exponential V–I characteristics

Cited by 6 publications

References 12 publications

On the Existence and Stability of Periodic Solutions for a Nonlinear Neutral Functional Differential Equation

On the Existence and Stability of Periodic Solutions for a Nonlinear Neutral Functional Differential Equation

Periodicity and stability in neutral equations by Krasnoselskii’s fixed point theorem

Recent Advances in Oscillation Theory 2011

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