Voir la notice de l'article provenant de la source Numdam
@article{RSMUP_1988__80__95_0, author = {Fernandes, M. L. C. and Zanolin, F.}, title = {Repelling conditions for boundary sets using {Liapunov-like} functions. {I.} - {Flow-invariance,} terminal value problem and weak persistence}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, pages = {95--116}, publisher = {Seminario Matematico of the University of Padua}, volume = {80}, year = {1988}, mrnumber = {988116}, zbl = {0672.34048}, language = {en}, url = {http://geodesic.mathdoc.fr/item/RSMUP_1988__80__95_0/} }
TY - JOUR AU - Fernandes, M. L. C. AU - Zanolin, F. TI - Repelling conditions for boundary sets using Liapunov-like functions. I. - Flow-invariance, terminal value problem and weak persistence JO - Rendiconti del Seminario Matematico della Università di Padova PY - 1988 SP - 95 EP - 116 VL - 80 PB - Seminario Matematico of the University of Padua UR - http://geodesic.mathdoc.fr/item/RSMUP_1988__80__95_0/ LA - en ID - RSMUP_1988__80__95_0 ER -
%0 Journal Article %A Fernandes, M. L. C. %A Zanolin, F. %T Repelling conditions for boundary sets using Liapunov-like functions. I. - Flow-invariance, terminal value problem and weak persistence %J Rendiconti del Seminario Matematico della Università di Padova %D 1988 %P 95-116 %V 80 %I Seminario Matematico of the University of Padua %U http://geodesic.mathdoc.fr/item/RSMUP_1988__80__95_0/ %G en %F RSMUP_1988__80__95_0
Fernandes, M. L. C.; Zanolin, F. Repelling conditions for boundary sets using Liapunov-like functions. I. - Flow-invariance, terminal value problem and weak persistence. Rendiconti del Seminario Matematico della Università di Padova, Tome 80 (1988), pp. 95-116. http://geodesic.mathdoc.fr/item/RSMUP_1988__80__95_0/
[1] Gewöhnliche Differentialgleichungen, Walter de Gruyter, Berlin, 1983. | Zbl | MR
,[2] A. CELLINA, Differential inclusions, Springer-Verlag, Berlin and New York, 1984. | Zbl | MR
-[3] Uniqueness for ordinary differential equations, Math. Systems Theory, 9 (1976), pp. 359-367. | Zbl | MR
- - ,[4] A uniqueness theorem for y' = f (x, y) using a certain factorization of f, J. Differential Equations, 7 (1970), pp. 227-231. | Zbl | MR
,[5] Uniformly persistent systems, Proc. Amer. Math. Soc., 96 (1986), pp. 425-430. | Zbl | MR
- - ,[6] Sui teoremi d'unicità relativi ad un'equazione differenziale ordinata del primo ordine, Giorn. Mat. Battaglini, 78 (1948), pp. 193-215. | Zbl | MR
,[7] Nonlinear singular perturbation phenomena: theory and applications, Springer-Verlag, Berlin and New York, 1984. | Zbl | MR
- ,[8] A generalization of Peano's existence theorem and flow-invariance, Proc. Amer. Math. Soc., 36 (1972), pp. 151-155. | Zbl | MR
,[9] Invariant sets and periodic solutions for differential systems, Magister Ph. Thesis, I.S.A.S., Trieste, 1986.
,[10] Remarks on strongly flow-invariant sets, J. Math. Anal. Appl., 128 (1987), pp. 176-188. | Zbl | MR
- ,[11] On periodic solutions, in a given set, for differential systems (preprint). | Zbl | MR
- ,[12] Repelling conditions for boundary sets using Liapunov-like functions. - II: Persistence and periodic solutions (preprint). | Zbl | MR
- ,[13] Uniformly persistent semi-dynamical systems, Proc. Amer. Math. Soc. (to appear). | Zbl | MR
,[14] Mathematical analysis of some three species food-chain models, Math. Biosci., 33 (1977), pp. 257-276. | Zbl | MR
- ,[15] Coincidence degree and nonlinear differential equations, Lecture Notes in Mathematics, vol. 568, Springer-Verlag, Berlin, 1977. | Zbl | MR
- ,[16] A generalization of the Naguno uniqueness criterion, Proc. Amer. Math. Soc., 70 (1978), pp. 166-172. | Zbl | MR
,[17] Strongly flow-invariant sets, Appl. Analysis, 10 (1980), pp. 285-293. | Zbl | MR
,[18] Persistence in food webs-1. Lotka Volterra food chains, Bull. Math. Biol., 41 (1979), pp. 877-891. | Zbl | MR
- ,[19] Aspects of convexity and its applications, Expo. Math., 2 (1984), pp. 47-83. | Zbl | MR
,[20] A comparison principle for terminal value problems in ordinary differential equations, Trans. Amer. Math. Soc., 169 (1972), pp. 49-57. | Zbl | MR
,[21] Ordinary differential equations, Wiley, New York, 1964. | Zbl | MR
,[22] A general cooperation theorem for hypercycles, Monatsh. Math., 91 (1981), pp. 233-240. | Zbl | MR | EuDML
,[23] A theorem on average Liapunov functions, Monatsh. Math., 98 (1984), pp. 267-275. | Zbl | MR | EuDML
,[24] The operator of translation along trajectories of of differential equations, Amer. Math. Soc., Providence, R.I., 1968. | MR
,[25] Differential and integral inequalities, vol. I, Academic Press, New York, 1969. | Zbl | MR
- ,[26] The stability of dynamical systems, Reg. Conf. Ser. in Math., SIAM, Philadelp ia, 1976. | MR
,[27] Contributions to stability theory, Ann. Math., 64 (1956), pp. 182-206. | Zbl | MR
,[28] Functional analysis and boundary value problems, in « Studies in ordinary differential equations », vol. 14 (J. K. Hale, ed.), The Math. Assoc. of America, U.S.A., 1977. | Zbl | MR
,[29] Topological degree methods in nonlinear boundary value problems, Reg. Conf. Ser. in Math., CBMS no. 40, Amer. Math. Soc., Providence, R.I., 1979. | Zbl | MR
,[30] Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordnung, Japan J. Math., 3 (1926), pp. 107-112. | JFM
,[31] Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen, Proc. Phys.-Math. Soc. Japan, 24 (1942), pp. 551-559. | Zbl | MR
,[32] Ordinary differential equations in Rn, problems and methods, Springer-Verlag, Berlin and New York, 1984. | Zbl | MR
- - ,[33] Flow-invariant sets and differential inequalities in normed spaces, Appl. Analysis, 5 (1975), pp. 149-161. | Zbl | MR
- ,[34] Qualitative Theorie nichtlinearer Differentialgleichungen, Cremonese, Roma, 1963. | Zbl | MR
- - ,[35] Stability theory by Liapunov's Direct Method, Springer-Verlag, Berlin and New York, 1977. | Zbl | MR
- - ,[36] Famiglie ad un parametro di funzioni di Liapunov, nello studio della stabilità, Symposia Math., 6 (1971), pp. 309-330. | Zbl | MR
,[37] Dynamical systems under constant organization. - III: Cooperative and competitive behavior of hypercycles, J. Differential Equations, 32 (1979), pp. 357-368. | Zbl | MR
- - ,[38] A singular perturbation result for a system of ordinary differential equations, Bull. Math. Soc. Sci. Math. R. S. Roumanie, 27 (1983), pp. 273-282. | Zbl | MR
,[39] Solutions of Hallam's problem on the terminal comparison principle for ordinary differential inequalities, Trans. Amer. Math. Soc., 220 (1976), pp. 115-132. | Zbl | MR
,[40] Über die positive Invaranz einer abgeschlossenen Teilmenge eines Banachschen Raumes bezüglich der Differentialgleichung u' = f(t, u), J. reine angew. Math., 285 (1976), pp. 59-65. | Zbl | MR | EuDML
,[41] Existence and uniqueness of solutions of ordinary differential equations, Proc. Amer. Math. Soc., 23 (1969), pp. 27-33. | Zbl | MR
,[42] Invariance for ordinary differential equations, Math. Systems Theory, 1 (1967), pp. 353-372. | Zbl | MR
,[43] Stability theory by Liapunov's second method, The Math. Soc. of Japan, Tokyo, 1966. | Zbl | MR
,[44] Bound sets, periodic solutions and flow-invariance for ordinary differential equations in Rn some remarks, in « Colloquium on Topological Methods in BPVs for ODEs », ISAS, Rend. Ist. Mat. Univ. Trieste, 19 (1987), pp. 76-92. | Zbl | MR
,