Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Hans-Otto Walther"'
Autor:
Hans-Otto Walther
Publikováno v:
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2022, Iss 31, Pp 1-10 (2022)
For a differential equation with a state-dependent delay we show that the associated solution manifold $X_f$ of codimension 1 in the space $C^1([-r,0],\mathbb{R})$ is an almost graph over a hyperplane, which implies that $X_f$ is diffeomorphic to the
Externí odkaz:
https://doaj.org/article/cead8483f94e47d2a9b0490b1367b404
Autor:
Hans-Otto Walther
Publikováno v:
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2019, Iss 13, Pp 1-44 (2019)
In infinite-dimensional spaces there are non-equivalent notions of continuous differentiability which can be used to derive the familiar results of calculus up to the Implicit Function Theorem and beyond. For autonomous differential equations with va
Externí odkaz:
https://doaj.org/article/514135d9d8974b4082bc1f1c148747f3
Autor:
Hans-Otto Walther
Publikováno v:
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2016, Iss 85, Pp 1-29 (2016)
Consider the delay differential equation $x'(t)=f(x_t)$ with the history $x_t:(-\infty,0]\to\mathbb{R}^n$ of $x$ at 'time' $t$ defined by $x_t(s)=x(t+s)$. In order not to lose any possible entire solution of any example we work in the Fréchet space
Externí odkaz:
https://doaj.org/article/d43e943cd8914fe4ba7cf53ff87ccb20
Autor:
Hans-Otto Walther
Publikováno v:
Contemporary Mathematics. Fundamental Directions. 67:483-506
For autonomous delay differential equations x ' ( t ) = f ( x t ) {x'(t)=f(x_t)} we construct a continuous semiflow of continuously differentiable solution operators x 0 → x t {x_0 \to x_t} , t ≤ 0 {t \le 0} , on open subsets of the Fre´chet spa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e5c669e9ac4ef35e3395bf8692d3f649
https://doi.org/10.22363/2413-3639-2021-67-3-483-506
https://doi.org/10.22363/2413-3639-2021-67-3-483-506
Autor:
Hans-Otto Walther
Publikováno v:
Journal of Differential Equations. 293:226-248
Differential equations with state-dependent delays which generalize the scalar example (0) x ′ ( t ) = g ( x ( t ) , x ( t − d ( x t ) ) ) where g : R 2 → R and d : C ( [ − r , 0 ] , R ) → [ 0 , r ] are continuously differentiable, and with
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d2e7e157581277b9dc92d45cb5613032
https://doi.org/10.1016/j.jde.2021.05.024
https://doi.org/10.1016/j.jde.2021.05.024
Autor:
Hans-Otto Walther
Publikováno v:
Journal of Dynamics and Differential Equations. 34:2867-2900
We construct a delay functional d on an open subset of the space $$C^1_r=C^1([-r,0],\mathbb {R})$$ C r 1 = C 1 ( [ - r , 0 ] , R ) and find $$h\in (0,r)$$ h ∈ ( 0 , r ) so that the equation $$\begin{aligned} x'(t)=-x(t-d(x_t)) \end{aligned}$$ x ′
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d0eb846efc8bd62dd3654ca28b83550c
https://doi.org/10.1007/s10884-021-10008-2
https://doi.org/10.1007/s10884-021-10008-2
Autor:
Hans-Otto Walther
Publikováno v:
Journal of Differential Equations. 268:6821-6871
We construct a delay functional d U with values in ( 0 , r ) and find a positive number h r such that the negative feedback equation x ′ ( t ) = − x ( t − d U ( x t , r ) ) , with the segment x t , r : [ − r , 0 ] → R given by x t , r ( s )
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::723ea0671c8d530fe47d623f63932d66
https://doi.org/10.1016/j.jde.2019.11.079
https://doi.org/10.1016/j.jde.2019.11.079
Autor:
Hans-Otto Walther
Let $r>0, n\in\mathbb{N}, {\bf k}\in\mathbb{N}$. Consider the delay differential equation $$ x'(t)=g(x(t-d_1(Lx_t)),\ldots,x(t-d_{{\bf k}}(Lx_t))) $$ for $g:(\mathbb{R}^n)^{{\bf k}}\supset V\to\mathbb{R}^n$ continuously differentiable, $L$ a continuo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a031a80f11d290dcfcc5c4dbd870404c
http://arxiv.org/abs/2106.15956
http://arxiv.org/abs/2106.15956
Autor:
Hans-Otto Walther, Therese Mur Voigt
Publikováno v:
Journal of Dynamics and Differential Equations. 34:2581-2582
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::116090f1106df574d751ba06d208332d
https://doi.org/10.1007/s10884-021-10047-9
https://doi.org/10.1007/s10884-021-10047-9
Autor:
Hans-Otto Walther, Therese Mur Voigt
Publikováno v:
Journal of Dynamics and Differential Equations.
We consider a periodic function $$p:{\mathbb {R}}\rightarrow {\mathbb {R}}$$ p : R → R of minimal period 4 which satisfies a family of delay differential equations $$\begin{aligned} x'(t)=g(x(t-d_{\Delta }(x_t))),\quad \Delta \in {\mathbb {R}}, \en
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4ea02b58baa3268a8167dcbe7dfda050
https://doi.org/10.1007/s10884-020-09896-7
https://doi.org/10.1007/s10884-020-09896-7