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ABSTRACT Authors’ abstract: We explain why the Poincaré translation operators along the trajectories of upper-Carathéodory differential inclusions do not satisfy the exceptional cases, described in our earlier counter-examples, for upper... more
ABSTRACT Authors’ abstract: We explain why the Poincaré translation operators along the trajectories of upper-Carathéodory differential inclusions do not satisfy the exceptional cases, described in our earlier counter-examples, for upper semicontinuous maps. Such a discussion was stimulated by a recent paper of F. Obersnel and P. Omari, where they show that, for Carathéodory scalar differential equations, the existence of just one subharmonic solution (e.g. of order 2) implies the existence of subharmonics of all orders. We reprove this result alternatively just via a multivalued Poincaré translation operator approach. We also establish its randomized version on the basis of a universal randomization scheme developed recently by the first author.
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... JAN ANDRES⋆, LIBOR JÜTTNER and KAREL PASTOR Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejcín, Czech Republic. e-mail: andres@risc.upol.cz, juttner@avx.cz,... more
... JAN ANDRES⋆, LIBOR JÜTTNER and KAREL PASTOR Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc-Hejcín, Czech Republic. e-mail: andres@risc.upol.cz, juttner@avx.cz, pastor@inf.upol.cz ...
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The solvability of Floquet boundary value problems is investigated for upper-Cara- th eodory dieren tial inclusions by means of strictly localized C2-bounding functions. The existence of an entirely bounded solution is obtained in a... more
The solvability of Floquet boundary value problems is investigated for upper-Cara- th eodory dieren tial inclusions by means of strictly localized C2-bounding functions. The existence of an entirely bounded solution is obtained in a sequential way. Our criteria can be regarded as a multivalued extension of recent results of Mawhin and Thompson concerning periodic and bounded solutions of Carath eodory dieren tial equations. A simple illustrating example is supplied.
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The existence and localization of strong (Carathéodory) solutions is proved for a second-order Floquet problem in a Banach space. The result is obtained by combining a continuation principle together with a bounding (Liapunov-like)... more
The existence and localization of strong (Carathéodory) solutions is proved for a second-order Floquet problem in a Banach space. The result is obtained by combining a continuation principle together with a bounding (Liapunov-like) functions approach. The application of the Scorza–Dragoni type technique allows us to use strictly localized transversality conditions.
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In reply to a problem posed by Jean Leray in 1950, a nontrivial example of application of the Nielsen xed-point theory to dierential systems is given. So the existence of two entirely bounded solutions or three periodic (harmonic)... more
In reply to a problem posed by Jean Leray in 1950, a nontrivial example of application of the Nielsen xed-point theory to dierential systems is given. So the existence of two entirely bounded solutions or three periodic (harmonic) solutions of a planar system of ODEs is proved by means of the Nielsen number. Subsequently, in view of T. Matsuoka's results
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The experimental procedure concerning the text exploration is demonstrated step by step on an illustrative example. Our methodological note involves, besides other things, detailed linguistic, statistical, numerical and fractal analyses.... more
The experimental procedure concerning the text exploration is demonstrated step by step on an illustrative example. Our methodological note involves, besides other things, detailed linguistic, statistical, numerical and fractal analyses. It can be regarded as an instructive text for further linguistic experiments in this field.This paper is dedicated to Gabriel Altmann
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Applying a suitably modified Liapunov–Yoshizawa direct method [T. Yoshizawa, StabilityTheorybyLiapunov’sSecondMethod (Math. Soc. Japan, Tokyo, 1966)], a rigorous mathematical proof of dissipativity in the sense of Levinson [N. Rouche, P.... more
Applying a suitably modified Liapunov–Yoshizawa direct method [T. Yoshizawa, StabilityTheorybyLiapunov’sSecondMethod (Math. Soc. Japan, Tokyo, 1966)], a rigorous mathematical proof of dissipativity in the sense of Levinson [N. Rouche, P. Habets, and M. Laloy, StabilityTheorybyLiapunov’sDirectMethod (Springer, Berlin, 1977)] to the majority of effective optical processes has been carried out. The ability of an upper final estimation of the average number of
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Starting from the famous Schauder fixed-point theorem, we present some Lefschetz-like and Nielsen-like generalizations for certain ad- missible (multivalued) self-maps on metric ANR-spaces. These fixed-point principles are applied for... more
Starting from the famous Schauder fixed-point theorem, we present some Lefschetz-like and Nielsen-like generalizations for certain ad- missible (multivalued) self-maps on metric ANR-spaces. These fixed-point principles are applied for obtaining the existence and multiplicity results for boundary value problems.
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The relative Lefschetz and Nielsen fixed-point theorems are generalized for compact absorbing contractions on ANR-spaces and nilman- ifolds. The nontrivial Lefschetz number implies the existence of a fixed- point in the closure of the... more
The relative Lefschetz and Nielsen fixed-point theorems are generalized for compact absorbing contractions on ANR-spaces and nilman- ifolds. The nontrivial Lefschetz number implies the existence of a fixed- point in the closure of the complementary domain. The relative Nielsen numbers improve the lower estimate of the number of coincidences on the total space or indicate the location of fixed-points on
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ABSTRACT The Lefschetz and the Nielsen periodic point theorems are developed for compact absorbing contractions on ANRs. These results are reformulated in terms of discrete multivalued semi-dynamical systems. They are also applied to... more
ABSTRACT The Lefschetz and the Nielsen periodic point theorems are developed for compact absorbing contractions on ANRs. These results are reformulated in terms of discrete multivalued semi-dynamical systems. They are also applied to Carathéodory differential inclusions on tori for obtaining the existence and multiplicity results for boundary value problems.
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The authors consider the Floquet boundary value problem for second-order differential inclusions, where the right-hand side is an upper Carathéodory multivalued mapping. The main tool in proving existence and localization of solutions is... more
The authors consider the Floquet boundary value problem for second-order differential inclusions, where the right-hand side is an upper Carathéodory multivalued mapping. The main tool in proving existence and localization of solutions is topological degree theory connected with the guiding function method (so-called also potential method). Some illustrative examples are presented. The obtained results are essential and interesting. The presented proofs are technically complicated.