Riccati Technique and Asymptotic Behavior of Fourth-Order Advanced Differential Equations [PDF]
Mathematics, 2020 In this paper, we deal with the oscillation of fourth-order nonlinear advanced differential equations of the form r t y ‴ t α ′ + p t f y ‴ t + q t g y σ t = 0 .
Omar Bazighifan, Ioannis Dassios
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Modified Riccati technique for half-linear differential equations with delay
Electronic Journal of Qualitative Theory of Differential Equations, 2014 We study the half-linear differential equation $$ (r(t)\Phi(x'(t)))'+c(t)\Phi(x(\tau(t)))=0,\quad \Phi(x):=|x|^{p-2}x,\ p>1. $$ We formulate new oscillation criteria for this equation by comparing it with a certain ordinary linear or half-linear ...
Simona Fišnarová, Robert Marik
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Linearized Riccati Technique and (Non-)Oscillation Criteria for Half-Linear Difference Equations [PDF]
Advances in Difference Equations, 2008 We consider the half-linear second-order difference equation , , , where , are real-valued sequences. We associate with the above-mentioned equation a linear second-order difference equation and we show that oscillatory properties of the above ...
Fišnarová Simona +1 more
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Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations [PDF]
Mathematics, 2021 We study the second-order neutral half-linear differential equation and formulate new oscillation criteria for this equation, which are obtained through the use of the modified Riccati technique. In the first statement, the oscillation of the equation is ensured by the divergence of a certain integral.
Zuzana Pátíková, Simona Fišnarová
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A reduction technique for Generalised Riccati Difference Equations [PDF]
, 2013 This paper proposes a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalised discrete algebraic Riccati equation.
Ferrante, Augusto +1 more
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Computational Analysis of the Fractional Riccati Differential Equation with Prabhakar-type Memory
Mathematics, 2023 The key objective of the current work is to examine the behavior of the nonlinear fractional Riccati differential equation associated with the Caputo–Prabhakar derivative.
Jagdev Singh +2 more
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Exploring the exact solutions to the nonlinear systems with neural networks method [PDF]
Scientific ReportsThis paper explores the use of Riccati subequation neural networks to solve nonlinear partial differential equations modeling complex biological processes like cancer, brain function, and wound healing.
Jan Muhammad +3 more
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On oscillatory behaviour of third-order half-linear dynamic equations on time scales [PDF]
Opuscula Mathematica, 2022 In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first ...
Said R. Grace, Gokula Nanda Chhatria
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Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations [PDF]
Opuscula Mathematica, 2022 The proportional derivative (PD) controller of a differential operator is commonly referred to as the conformable derivative. In this paper, we derive a nonoscillation theorem for damped linear differential equations with a differential operator using ...
Kazuki Ishibashi
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A Riccati technique for proving oscillation of a half-linear equation
Electronic Journal of Differential Equations, 2008 In this paper we study the oscillation of solutions to the half-linear differential equation $$ (r(t)|y'|^{p-1}hbox{sgn} y)'+c(t)|y|^{p-1}hbox{sgn} y=0, $$ under the assumptions $int^infty r^{1/(1-p)}(s),ds0$, $p>1$.
Pavel Rehak
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