On Kneser solutions of the n -th order nonlinear differential inclusions

Martina Pavlačková

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 1, page 99-116
  • ISSN: 0011-4642

Abstract

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The paper deals with the existence of a Kneser solution of the n -th order nonlinear differential inclusion x ( n ) ( t ) ∈ - A 1 ( t , x ( t ) , ... , x ( n - 1 ) ( t ) ) x ( n - 1 ) ( t ) - ... - A n ( t , x ( t ) , ... , x ( n - 1 ) ( t ) ) x ( t ) for a.a. t ∈ [ a , ∞ ) , where a ∈ ( 0 , ∞ ) , and A i : [ a , ∞ ) × ℝ n → ℝ , i = 1 , ... , n , are upper-Carathéodory mappings. The derived result is finally illustrated by the third order Kneser problem.

How to cite

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Pavlačková, Martina. "On Kneser solutions of the $n$-th order nonlinear differential inclusions." Czechoslovak Mathematical Journal 69.1 (2019): 99-116. <http://eudml.org/doc/294160>.

@article{Pavlačková2019,
abstract = {The paper deals with the existence of a Kneser solution of the $n$-th order nonlinear differential inclusion \begin\{eqnarray\} \{x\}^\{(n)\}(t)\in -A\_\{1\}(t,x(t),\ldots ,x^\{(n-1)\}(t))\{x\}^\{(n-1)\}(t)-\ldots -A\_\{n\}(t,x(t),\ldots ,&x^\{(n-1)\}(t))x(t)\nonumber \\ &\text\{for a.a.\} \ t\in [a,\infty ),\nonumber \end\{eqnarray\} where $a\in (0,\infty )$, and $A_i\colon [a,\infty ) \times \mathbb \{R\}^\{n\}\rightarrow \mathbb \{R\}$, $i=1,\ldots ,n,$ are upper-Carathéodory mappings. The derived result is finally illustrated by the third order Kneser problem.},
author = {Pavlačková, Martina},
journal = {Czechoslovak Mathematical Journal},
keywords = {asymptotic $n$-th order vector problems; $R_\{\delta \}$-set; inverse limit technique; Kneser problem},
language = {eng},
number = {1},
pages = {99-116},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On Kneser solutions of the $n$-th order nonlinear differential inclusions},
url = {http://eudml.org/doc/294160},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Pavlačková, Martina
TI - On Kneser solutions of the $n$-th order nonlinear differential inclusions
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 99
EP - 116
AB - The paper deals with the existence of a Kneser solution of the $n$-th order nonlinear differential inclusion \begin{eqnarray} {x}^{(n)}(t)\in -A_{1}(t,x(t),\ldots ,x^{(n-1)}(t)){x}^{(n-1)}(t)-\ldots -A_{n}(t,x(t),\ldots ,&x^{(n-1)}(t))x(t)\nonumber \\ &\text{for a.a.} \ t\in [a,\infty ),\nonumber \end{eqnarray} where $a\in (0,\infty )$, and $A_i\colon [a,\infty ) \times \mathbb {R}^{n}\rightarrow \mathbb {R}$, $i=1,\ldots ,n,$ are upper-Carathéodory mappings. The derived result is finally illustrated by the third order Kneser problem.
LA - eng
KW - asymptotic $n$-th order vector problems; $R_{\delta }$-set; inverse limit technique; Kneser problem
UR - http://eudml.org/doc/294160
ER -

References

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