Voir la notice de l'article provenant de la source Library of Science
@article{DMDICO_2009_29_1_a7,
author = {Kubiaczyk, Ireneusz and Sikorska-Nowak, Aneta},
title = {Existence of solutions of the dynamic {Cauchy} problem on infinite time scale intervals},
journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization},
pages = {113--126},
publisher = {mathdoc},
volume = {29},
number = {1},
year = {2009},
zbl = {1198.34197},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a7/}
}
TY - JOUR AU - Kubiaczyk, Ireneusz AU - Sikorska-Nowak, Aneta TI - Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals JO - Discussiones Mathematicae. Differential Inclusions, Control and Optimization PY - 2009 SP - 113 EP - 126 VL - 29 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a7/ LA - en ID - DMDICO_2009_29_1_a7 ER -
%0 Journal Article %A Kubiaczyk, Ireneusz %A Sikorska-Nowak, Aneta %T Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals %J Discussiones Mathematicae. Differential Inclusions, Control and Optimization %D 2009 %P 113-126 %V 29 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a7/ %G en %F DMDICO_2009_29_1_a7
Kubiaczyk, Ireneusz; Sikorska-Nowak, Aneta. Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 29 (2009) no. 1, pp. 113-126. http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a7/
[1] R.P. Agarwal and M. Bohner, Basic calculus on time scales and some of its applications, Result Math. 35 (1999), 3-22.
[2] R.P. Agarwal, M. Bohner and A. Peterson, Inequalities on time scales: a survey, Math. Inequal. Appl. 4 (4) (2001), 535-557.
[3] R.P. Agarwal and D. O'Regan, Nonlinear boundary value problems on time scales, Nonlin. Anal. TMA 44 (2001), 527-535.
[4] R.P. Agarwal and D. O'Regan, Difference equations in Banach spaces, J. Austral. Math. Soc. (A) 64 (1998), 277-284.
[5] R.P. Agarwal and D. O'Regan, A fixed point approach for nonlinear discrete boundary value problems, Comp. Math. Appl. 36 (1998), 115-121.
[6] R.P. Agarwal, D. O'Regan and S.H. Saker, Properties of bounded solutions of nonlinear dynamic equations on time scales, Can. Appl. Math. Q. 14 (1) (2006), 1-10.
[7] E. Akin-Bohner, M. Bohner and F. Akin, Pachpate inequalities on time scale, J. Inequal. Pure and Appl. Math. 6 (1) Art. 6, (2005).
[8] A. Ambrosetti, Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Univ. Padova 39 (1967), 349-361.
[9] G. Aslim and G.Sh. Guseinov, Weak semiring, ω-semirings, and measures, Bull. Allahabad Math. Soc. 14 (1999), 1-20.
[10] B. Aulbach and S. Hilger, Linear dynamic processes with inhomogeneous time scale, Nonlinear Dynamics and Quantum Dynamical Systems, Akademie Verlag, Berlin, 1990.
[11] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math. 60, Dekker, New York and Basel, 1980.
[12] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkäuser, 2001.
[13] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkäuser, Boston, 2003.
[14] A. Cellina, On existence of solutions of ordinary differential equations in Banach spaces, Func. Ekvac. 14 (1971), 129-136.
[15] M. Cichoń, On solutions of differential equations in Banach spaces, Nonlin. Anal. TMA 60 (2005), 651-667.
[16] M. Dawidowski, I. Kubiaczyk and J. Morchało, A discrete boundary value problem in Banach spaces, Glasnik Mat. 36 (2001), 233-239.
[17] R. Dragoni, J.W. Macki, P. Nistri and P. Zecca, Solution Sets of Differential Equations in Abstract Spaces, Longmann, 1996.
[18] L. Erbe and A. Peterson, Green's functions and comparison theorems for differential equations on measure chains, Dynam. Contin. Discrete Impuls. Systems 6 (1) (1999), 121-137.
[19] G.Sh. Guseinov, Integration on time scales, J. Math. Anal. Appl. 285 (2003), 107-127.
[20] C. Gonzalez and A. Jimenez-Meloda, Set-contractive mappings and difference equations in Banach spaces, Comp. Math. Appl. 45 (2003), 1235-1243.
[21] S. Hilger, Ein Maßkettenkalkül mit Anvendung auf Zentrumsmannigfaltigkeiten, PhD thesis, Universität at Würzburg, 1988.
[22] S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18-56.
[23] B. Kaymakcalan, V. Lakshmikantham and S. Sivasundaram, Dynamical Systems on Measure Chains, Kluwer Akademic Publishers, Dordrecht, 1996.
[24] I. Kubiaczyk, On the existence of solutions of differential equations in Banach spaces, Bull. Polish Acad. Sci. Math. 33 (1985), 607-614.
[25] B.N. Sadovskii, Limit-compact and condensing operators, Russian Math. Surveys 27 (1972), 86-144.
[26] S. Szufla, Measure of noncompanctness and ordinary differential equations in Banach spaces, Bull. Polish Acad. Sci. Math. 19 (1971), 831-835.