An encounter in the realm of Structural Stability between a qualitative theory for geometric shapes and one for the integral foliations of differential equations [PDF]
, 2020 This evocative essay focuses on some landmarks that led the author to the study of principal curvature configurations on surfaces in $\mathbb R^3$, their structural stability and generic properties. The starting point was an encounter with the book of D. Struik and the reading of the references to the works of Euler, Monge and Darboux found there.
Jorge Sotomayor
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A Stability Theory for Integral Equations [PDF]
Journal of Integral Equations and Applications, 1994 The most important thing we have to know in stability theory of differential equations is the set of what we call equilibrium points. A useful meaning in developing such a theory is introduced in the present paper and it is termed ``near equilibrium''. Briefly speaking given an integral equation \(x(t)=a(t)-\int^t_{\alpha(t)} Q (t, s, x(s))ds\) we say ...
Burton, T.A., Furumochi, Tetsuo
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Stability for nonlinear generalized ODEs and for retarded Volterra-Stieltjes integral equations and control theory for these equations and for dynamic equations on time scale [PDF]
, 2021 Fernanda Andrade da Silva
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Karpatsʹkì Matematičnì Publìkacìï, 2022 The aim of the present paper is to investigate of some properties of periodic solutions of a nonlinear autonomous parabolic systems with a periodic condition.
I.I. Klevchuk
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Continuous operator method application for direct and inverse scattering problems
Журнал Средневолжского математического общества, 2021 We describe the continuous operator method for solution nonlinear operator equations and discuss its application for investigating direct and inverse scattering problems.
Boykov Ilya V. +3 more
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An approximation method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory [PDF]
Proceedings of the 45th IEEE Conference on Decision and Control, 2006 In this report, a method for approximating the stabilizing solution of the Hamilton-Jacobi equation for integrable systems is proposed using symplectic geometry and a Hamiltonian perturbation technique. Using the fact that the Hamiltonian lifted system of an integrable system is also integrable, the Hamiltonian system (canonical equation) that is ...
Sakamoto, N., van der Schaft, Arjan
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Approximate Methods for Solving Linear and Nonlinear Hypersingular Integral Equations
Axioms, 2020 We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides.
Ilya Boykov +2 more
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Journal of Function Spaces, 2023 In the present paper, a new efficient technique is described for solving nonlinear mixed partial integrodifferential equations with continuous kernels.
Abeer M. Al-Bugami +2 more
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Nonlinear Engineering, 2023 The present article proposes a new-integral transform-based variational iteration technique (NTVIT) to study the behavior of higher-order nonlinear time-fractional delayed differential equations.
Singh Brajesh K. +4 more
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Positive Invertibility of Matrices and Exponential Stability of Linear Stochastic Systems with Delay
International Journal of Differential Equations, 2022 The work addresses the exponential moment stability of solutions of large systems of linear differential Itô equations with variable delays by means of a modified regularization method, which can be viewed as an alternative to the technique based on ...
Ramazan Kadiev, Arcady Ponosov
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