A reduction technique for generalised Riccati difference equations arising in linear-quadratic optimal control [PDF]
2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012 In this paper we develop a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a decomposition method for the generalised Riccati difference equation that isolates its nilpotent part, which becomes constant in a number of iteration steps equal to the nilpotency ...
Lorenzo Ntogramatzidis +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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Oscillation Criteria for PDE with p-Laplacian via the Riccati Technique
Journal of Mathematical Analysis and Applications, 2000 The aim of this paper is to give some oscillation criteria for the following partial differential equation (PDE) with \(p\)-Laplacian: \[ \text{div}(\|\nabla u\|^{p-2}\nabla u)+ c(x)\phi(u)=0,\tag{1} \] where \(p>1\) and \(\phi(u)=|u|^{p-2}u\). The equation (1) is said to be oscillatory if every solution \(u\) is oscillatory, i.e., \(u\) has a zero in \
Robert Marik
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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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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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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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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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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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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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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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