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V. Filippov (1998)
Basic topological structures of ordinary differential equations
Владимир Филиппов, V. Filippov (2002)
О существовании периодических решений уравнений с сильно растущей главной частью@@@On the existence of periodic solutions of equations with strongly increasing principal partMatematicheskii Sbornik, 193
Владимир Филиппов, V. Filippov (1997)
О гомологических свойствах множеств решений обыкновенных дифференциальных уравнений@@@Homology properties of the sets of solutions to ordinaryMatematicheskii Sbornik, 188
A. Granas, R. Guenther, John Lee (1978)
On a theorem of S. BernsteinPacific Journal of Mathematics, 74
H. Seifert, W. Threlfall (1934)
Lehrbuch der Topologie
Владимир Филиппов, V. Filippov (2003)
О спектре Фучика и периодических решениях@@@On Fucik Spectra and Periodic Solutions, 73
A. Granas, R. Guenther, John Lee (1983)
Topological transversality. II. Applications to the Neumann problem for y′′ = f(t, y, y′)Pacific Journal of Mathematics, 104
Differential Equations, Vol. 41, No. 6, 2005, pp. 791–796. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 6, 2005, pp. 755–760. Original Russian Text Copyright c 2005 by Zuev, Filippov. ORDINARY DIFFERENTIAL EQUATIONS On the Neumann Problem for an Ordinary Di erential Equation with Discontinuous Right-Hand Side A. V. Zuev and V. V. Filippov Moscow State University, Moscow, Russia Received February 11, 2004 In the present paper, we continue the development of the theory of boundary value problems for ordinary di erential equations and for inclusions with discontinuous right-hand sides [1{5] based on the further development of a new version of the method of shifts along trajectories. Compared with the well-known method of shifts, the new version is characterized by the fact that a \shift" is assigned to a solution rather than a point of the phase space. This has become possible owing to the investigation [1, 6{8] of topological properties of solution spaces. Here we also clarify the speci c properties appearing in the proof of the existence of a solution of the Neumann problem 00 0 x 2 g (t;x;x ); (1a) 0 0 x (0) = r; x (T )= s; (1b) where g : U !
Differential Equations – Springer Journals
Published: Jul 27, 2005
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