On Kneser solutions of the $n$-th order nonlinear differential inclusions
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 99-116
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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 ,^{(n-1)}(t))x(t)\nonumber \\ \text {for a.a.} \ t\in [a,\infty ),\nonumber \end {eqnarray} where $a\in (0,\infty )$, and $A_i\colon [a,\infty ) \times \mathbb {R}^{n}\to \mathbb {R}$, $i=1,\ldots ,n,$ are upper-Carathéodory mappings. The derived result is finally illustrated by the third order Kneser problem.
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 ,^{(n-1)}(t))x(t)\nonumber \\ \text {for a.a.} \ t\in [a,\infty ),\nonumber \end {eqnarray} where $a\in (0,\infty )$, and $A_i\colon [a,\infty ) \times \mathbb {R}^{n}\to \mathbb {R}$, $i=1,\ldots ,n,$ are upper-Carathéodory mappings. The derived result is finally illustrated by the third order Kneser problem.
DOI :
10.21136/CMJ.2018.0191-17
Classification :
34A60, 34B15, 34B40
Keywords: asymptotic $n$-th order vector problems; $R_{\delta }$-set; inverse limit technique; Kneser problem
Keywords: asymptotic $n$-th order vector problems; $R_{\delta }$-set; inverse limit technique; Kneser problem
@article{10_21136_CMJ_2018_0191_17,
author = {Pavla\v{c}kov\'a, Martina},
title = {On {Kneser} solutions of the $n$-th order nonlinear differential inclusions},
journal = {Czechoslovak Mathematical Journal},
pages = {99--116},
year = {2019},
volume = {69},
number = {1},
doi = {10.21136/CMJ.2018.0191-17},
mrnumber = {3923578},
zbl = {07088773},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0191-17/}
}
TY - JOUR AU - Pavlačková, Martina TI - On Kneser solutions of the $n$-th order nonlinear differential inclusions JO - Czechoslovak Mathematical Journal PY - 2019 SP - 99 EP - 116 VL - 69 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0191-17/ DO - 10.21136/CMJ.2018.0191-17 LA - en ID - 10_21136_CMJ_2018_0191_17 ER -
%0 Journal Article %A Pavlačková, Martina %T On Kneser solutions of the $n$-th order nonlinear differential inclusions %J Czechoslovak Mathematical Journal %D 2019 %P 99-116 %V 69 %N 1 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0191-17/ %R 10.21136/CMJ.2018.0191-17 %G en %F 10_21136_CMJ_2018_0191_17
Pavlačková, Martina. On Kneser solutions of the $n$-th order nonlinear differential inclusions. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 99-116. doi: 10.21136/CMJ.2018.0191-17
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