Czechoslovak Mathematical Journal, Vol. 69, No. 1, pp. 99-116, 2019
On Kneser solutions of the $n$-th order nonlinear differential inclusions
Martina Pavlačková
Received April 24, 2017. Published online July 13, 2018.
Abstract: The paper deals with the existence of a Kneser solution of the $n$-th order nonlinear differential inclusion
$\align{x}^{(n)}(t)\in-A_1(t,x(t),\ldots,x^{(n-1)}(t))x^{(n-1)}(t)-\ldots-A_n(t,x(t),\ldots,&x^{(n-1)}(t))x(t) \\
&\text{for a.a.} t\in[a,\infty),$ where $a\in(0,\infty)$, and $A_i [a,\infty) \times\mathbb{R}^n\to\mathbb{R}$, $i=1,\ldots,n,$ are upper-Carathéodory mappings. The derived result is finally illustrated by the third order Kneser problem.
Keywords: asymptotic $n$-th order vector problems; $R_{\delta}$-set; inverse limit technique; Kneser problem
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Affiliations: Martina Pavlačková, Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic, e-mail: martina.pavlackova@upol.cz
