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

Pavlačková, Martina

Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 99-116.

Résumé

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.

Détail

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