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1996 | 35 | 1 | 109-118
Tytuł artykułu

Partially dissipative periodic processes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.
Rocznik
Tom
35
Numer
1
Strony
109-118
Opis fizyczny
Daty
wydano
1996
Twórcy
autor
  • Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejčín, Czech Republic
  • Department of Mathematics, Nicolas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  • Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, 80-952 Gdańsk-Oliwa, Poland
Bibliografia
  • [1] J. Andres, Asymptotic properties of solutions to quasi-linear differential systems., J. Comp. Appl. Math. 41 (1991), 56-64.
  • [2] J. Andres, Transformation theory for nondissipative systems: Some remarks and simple application in examples, Acta UPO 111, Phys. 32 (1993), 125-132.
  • [3] J. Andres, Large-period forced oscillations to higher-order pendulum-type equations, to appear in Diff. Eqns and Dynam. Syst.
  • [4] J. Andres, M. Gaudenzi and F. Zanolin, A transformation theorem for periodic solutions of nondissipative systems, Rend. Sem. Mat. Univers. Politecn. Torino 48(2) (1990), 171-186.
  • [5] R. Bader and W. Kryszewski, Fixed point index for compositions of set-valued maps with proximally ∞-connected values on arbitrary ANR's, Set Valued Analysis 2(3) (1994), 459-480.
  • [6] A. Bressan, Upper and lower semicontinuous differential inclusions. A unified approach, Controllability and Optimal Control, H. Sussmann (ed.), M. Dekker, 1990, 21-31.
  • [7] A. Capietto and B. M. Garay, Saturated invariant sets and boundary behaviour of differential systems, J. Math. Anal. Appl. 176(1) (1993), 166-181.
  • [8] M. L. C. Fernandes, Uniform repellers for processes with application to periodic differential systems, J. Diff. Eq. 86 (1993), 141-157.
  • [9] M. L. C. Fernandes and F. Zanolin, Repelling conditions for boundary sets using Liapunov-like functions II: Persistence and periodic solutions, J. Diff. Eq. 86 (1993), 33-58.
  • [10] L. Górniewicz, Topological Approach to Differential Inclusions, Preprint No. 104 (November 1994), University of Gdańsk, 1-66.
  • [11] L. Górniewicz, A. Granas and W. Kryszewski, On the homotopy method in the fixed point index theory of multivalued mappings of compact ANR's, J. Math. Anal. Appl. 161 (1991), 457-473.
  • [12] L. Górniewicz and S. Plaskacz, Periodic solutions of differential inclusions in $R^n$, Boll. U. M. I. 7-A (1993), 409-420.
  • [13] J. K. Hale, Asymptotic Behavior of Dissipative Systems, MSM 25, AMS, Providence, R. I., 1988.
  • [14] J. K. Hale, J. P. LaSalle and M. Slemrod, Theory of general class of dissipative processes, J. Math. Anal. Appl. 39(1) (1972), 117-191.
  • [15] J. K. Hale and O. Lopes, Fixed-point theorems and dissipative processes, J. Diff. Eq. 13 (1973), 391-402.
  • [16] J. Hofbauer, An index theorem for dissipative semiflows, Rocky Mountain J. Math. 20(4) (1993), 1017-1031.
  • [17] J. Hofbauer and K. Sigmund, Dynamical Systems and the Theory of Evolution, Cambrige Univ. Press, Cambrige, 1988.
  • [18] A. M. Krasnosel'skiĭ, M. A. Krasnosel'skiĭ and J. Mawhin, On some conditions of forced periodic oscillations, Diff. Integral Eq. 5(6) (1992), 1267-1273.
  • [19] A. M. Krasnosel'skiĭ, J. Mawhin, M. A. Krasnosel'skiĭ and A. Pokrovskiĭ, Generalized guiding functions in a problem on high frequency forced oscillations, Rapp. no 222 - February 1993, Sm. Math., Inst. de Math. Pure et Appl. UCL.
  • [20] M. A. Krasnosel'skiĭ, J. Mawhin and A. Pokrovskiĭ, New theorems on forced periodic oscillations and bounded solutions, Doklady AN SSSR 321(3) (1991) 491-495 (in Russian).
  • [21] N. Levinson, Transformation theory of non-linear differential equations of the second order, Ann. of Math. 45 (1944), 723-737.
  • [22] V. V. Rumyantsev and A. S. Oziraner, The Stability and Stabilization of Motion with Respect to Some of the Variables, Nauka, Moscow, 1987 (in Russian).
  • [23] G. R. Sell, Periodic solutions and asymptotic stability, J. Diff. Eq. 2(2) (1966), 143-157.
  • [24] R. Srzednicki, Periodic and bounded solutions in blocks for time-periodic nonautonomous ordinary differential equations, Nonlinear Anal., T.M.A. 22, 6 (1994), 707-737.
  • [25] V. I. Vorotnikov, Stability of Dynamical Systems with Respect to Some of the Variables, Nauka, Moscow, 1991 (in Russian).
  • [26] T. Yoshizawa, Stability Theory and Existence of Periodic Solutions and Almost Periodic Solutions, Springer, Berlin, 1975.
  • [27] F. Zanolin, Permanence and positive periodic solutions for Kolmogorov competing species systems, Preprint of SISSA, Ref. 144/91/M.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv35i1p109bwm
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