Filippov's theorem
WebFeb 1, 2024 · The Poincaré map with its analytical property and the problem of Hopf bifurcation have been studied in Coll et al. (2001) [3] and Filippov (1988) [6] for general systems and in Zou et al. (2006 ... WebA.1. Proof of Theorem 1 We rst provide the detailed background information about the theorem which will be used to prove the existence and uniqueness of the solution of the uid model. A.1.1. Theorem 3 in x10 of Filippov (1988) Here, we translate the conditions in part 3 of x10 of Filippov (1988) for applying the theorem to our problem.
Filippov's theorem
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WebApr 1, 2024 · Next, we briefly recall the key points of Filippov theory. Suppose one has the piecewise smooth ODE (2) R −: x ˙ = f − ( x) h ( x) < 0, R +: x ˙ = f + ( x) h ( x) > 0, with x ∈ R n, f ±: R n → R n, h: R n → R, and Σ as in (1). Here, f ± are assumed to be C 1 (at least), and h is at least C 2 in a neighborhood of Σ. WebThe implicit function theorem proved in 1959 by A. F. Filippov in 1wx serves as an important tool in the optimal control theory. It assumes however some continuity …
WebIn this paper, we present an impulsive version of Filippov’s Theorem for fractional differential inclusions of the form: Dα ∗ y(t) ∈ F(t,y(t)), a.e. t ∈ J\{t1,...,tm}, α ∈ (1,2],) − … WebFilip Genov. 25+ years in banking, innovations and technology. Non-institutional special adviser to the President of Bulgaria for financial technologies, banking and innovations. …
Webrespectively. Then, we shall be concerned with Filippov’s theorem for impulsive differ-ential inclusions with fractional order in Section 4. 2 Preliminaries In this section, we introduce notations, definitions, and preliminary facts that will be used in the remainder of this paper. Let ACi([0,b],Rn) be the space of functions WebThe celebrated Filippov theorem (see e.g. [AF90]) implies that PT F holds true in the case when F is Lipschitz in the state variable and measurable in time. The importance of …
WebCurve theorem proof. Aleksei Fedorovich Filippov (Russian: Алексей Фёдорович Филиппов; 29 September 1923 – 10 October 2006) was a Russian mathematician, who worked on differential equations, differential inclusions, diffraction theory, and numerical methods . A. F. Filippov was born in Moscow in 1923. After serving in ...
WebFilippov existence theorem for Pontryagin's problems (U(t, x) compact), existence theorems for usual Lagrange problems (U = Em), and the Nagumo-Tonelli existence … townhomes of lake seminoleWebDec 4, 2024 · Theorem 5.4. The infinitesimals of equivalent finite order deformations of a Filippov algebroid (A, [,\ldots ,],a) belong to the same cohomology class in H^2_F (A). A deformation of order 1 of a Filippov algebroid is called an infinitesimal deformation. townhomes of newtown crossing lexington kyWebMar 8, 2024 · With this new index definition, we provide a version of the Poincaré--Hopf Theorem for Filippov vector fields. Consequently, we also get a Hairy Ball Theorem in … townhomes of oakley richmond vaWebJan 10, 2024 · Abstract: The solution existence of finite horizon optimal economic growth problems is studied by invoking Filippov's Existence Theorem for optimal control … townhomes of north cantonWebwhich are Filippov type existence results for this problem. The first one is obtained by the application of the set- valued contraction principle in the space of derivatives of solutions … townhomes of san simeonWebNext we can give the proof for Theorem 1 Proof. Applying Filippov regularization, the right hand side of (1) transforms into the set-valued function Fgiven by (5). Fis a convex u.s.c. (Proposition 1) and non-empty valued function (Remark 3). Therefore, Theorem 2 can be used and the IVP (1) becomes a continuous IVP of fractional order to which ... townhomes of oriole associationWebin [33, Theorem 17] (resp. in [35, Theorem 4.2]). W e conclude this section by pointing out that a large number of publications has been dedicated to the numerical study of fractional optimal ... townhomes of oriole association inc