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Czechoslovak Mathematical Journal

, Volume 69, Issue 1, pp 99–116 | Cite as

On Kneser Solutions of the n-th Order Nonlinear Differential Inclusions

  • Martina PavlačkováEmail author
Article
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Abstract

The paper deals with the existence of a Kneser solution of the n-th order nonlinear differential inclusion
$${x^{(n)}}(t) \in - {A_1}(t,x,(t),...,{x^{(n - 1)}}(t)){x^{(n - 1)}}(t) - ... - {A_n}(t,x(t),...,{x^{(n - 1)}}(t))x(t)\;\text{for}\;\text{a.a.}\;t\; \in [a,\infty ),$$
where a ∈ (0,∞), and Ai: [a,∞) × ℝn → ℝ, i = 1,..., n, are upper-Carathéodory mappings. The derived result is finally illustrated by the third order Kneser problem.

Keywords

asymptotic n-th order vector problems Rδ-set inverse limit technique Kneser problem 

MSC 2010

34A60 34B15 34B40 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Department of Mathematical Analysis and Applications of Mathematics, Faculty of SciencePalacký UniversityOlomoucCzech Republic

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