Applicable Fixed Point Principles

Andres, Jan

doi:10.1007/1-4020-3222-6_19

Cited by 3 publications

(3 citation statements)

References 32 publications

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“…Since Q 1 is an AR-space, the related fixed point index satisfies ind(T π 4 , Q 1 ) = 1 (see [4,7]). …”

Section: Corollary 1 Let Inequalitiesmentioning

confidence: 99%

“…[1,4,7]) for operator differential inclusions with suitable constraints, and then • to construct, on the basis of this method, a nontrivial example of a system of differential inclusions which has at least two periodic solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Then the same argument as above shows thatQ is invariant under the solution operator T π/4 . By the homotopy and reduction properties of the related welldefined fixed point index, (cf., e.g.,[4,7]), we arrive at ind(T π 4 |Q,Q) = ind(T 0 |Q,Q) = ind(L, Q) = 2.…”

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confidence: 97%

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Nontrivial application of Nielsen theory to differential systems

Andres

Fürst

2006

Journal of Differential Equations

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In reply to a problem of Jean Leray concerning application of the Nielsen theory to differential systems for obtaining multiplicity results, we present a nontrivial example of such an application. The emphasis is on the parameter space in order to ensure that no subdomain becomes subinvariant under the related Hammerstein solution operator. To achieve this goal, we develop a general method applicable also for ordinary differential equations with or without uniqueness as well as for upper-Carathéodory differential inclusions. We are not aware that any alternative approach can be employed, even in the single-valued case.

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“…Since Q 1 is an AR-space, the related fixed point index satisfies ind(T π 4 , Q 1 ) = 1 (see [4,7]). …”

Section: Corollary 1 Let Inequalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nontrivial application of Nielsen theory to differential systems

Andres

Fürst

2006

Journal of Differential Equations

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Chapter 1 Topological Principles for Ordinary Differential Equations

Andres

2006

Handbook of Differential Equations: Ordinary Differential Equations

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Multivalued Fractals and Hyperfractals

Andres

Rypka

2012

Int. J. Bifurcation Chaos

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A new class of fractals called hyperfractals is systematically investigated. Their underlying fractals in supporting spaces are multivalued fractals developed by ourselves in our earlier papers [Andres & Fiser, 2004; Andres et al., 2005]. In the case of uniqueness, they also coincide with the supports of invariant measures of the associated Markov–Feller hyperoperators. We prove their existence by means of fixed point theorems in hyperspaces and calculate, in particular cases of generating hypermaps, their Hausdorff dimension. Two illustrative examples are supplied.

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Applicable Fixed Point Principles

Cited by 3 publications

References 32 publications

Nontrivial application of Nielsen theory to differential systems

Nontrivial application of Nielsen theory to differential systems

Chapter 1 Topological Principles for Ordinary Differential Equations

Multivalued Fractals and Hyperfractals

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