- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 15:09:50
8
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=3&iss=1&update_since=2024-03-29
Zeitschrift für Analysis und ihre Anwendungen
Z. Anal. Anwend.
ZAA
0232-2064
1661-4534
Partial differential equations
Ordinary differential equations
Integral equations
Numerical analysis
10.4171/ZAA
http://www.ems-ph.org/doi/10.4171/ZAA
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2006)
3
1984
1
Some estimates of the norms of derivatives of holomorphic functions, and their application to initial value problems (in Russian)
G.F.
Mandzhavidze
Tbilisi State University, TBILISI, GEORGIA
Wolfgang
Tutschke
Technische Universität Graz, GRAZ, AUSTRIA
The paper deals with the solution of initial value problems in scales of Banach spaces of generalized analytic functions. To this end a priori estimates of holomorphic functions are given, which allow to solve the initial value problems mentioned above in $L_p$-spaces.
General
1
5
10.4171/ZAA/86
http://www.ems-ph.org/doi/10.4171/ZAA/86
Riemannfunktionen and Differentialoperatoren
Karl Wilhelm
Bauer
Universität Graz, GRAZ, AUSTRIA
It is shown that the complex Riemann function of a formally hyperbolic differential equation can be represented by a differential operator if a representation of solutions is possible by at least one differential operator. The application of this method is illustrated by several examples.
General
7
17
10.4171/ZAA/87
http://www.ems-ph.org/doi/10.4171/ZAA/87
Flächensätze für quasikonform fortsetzbare Abbildungen
Erich
Hoy
, FRIEDBERG, GERMANY
In this paper an extension of the area principle to conformal mappings with a $Q_j$-quasiconformal continuation into the component $\mathcal B_j$ of the complement of a region $\mathcal G$ is given. A generalized area-theorem is proved for these mappings. The inequalities are sharp; the extrernal functions are connected with the solution of the equation $w_{\bar z} = \mu (z) \bar {w_z}$ with $\mu (z)$ being a piecewise constant function. These area theorems are applied to the estimations of the ranges of the coefficient for $z^{-1}$ of the Laurent expansion in the neighbourhood of infinity, the Schwarzian derivative and Golusin’s functional. Finally the possibility of an extension to conformal mappings with a quasiconformal continuation is shown. For Grunsky’s regions these inequalities are asymptotically sharp, if the restriction of the dilatation converges to a constant.
General
19
31
10.4171/ZAA/88
http://www.ems-ph.org/doi/10.4171/ZAA/88
Asymptotic conditions at the two first eigenvalues for the periodic solutions of Liénard differential equations and an inequality of E. Schmidt
C.P.
Gupta
Northern Illinois University, DEKALB, UNITED STATES
Jean
Mawhin
Université Catholique de Louvain, LOUVAIN-LA-NEUVE, BELGIUM
We study the periodic boundary problem $$x’’(t) + f(x(t)) x’(t) + g(t, x(t)) = e(t),$$ $$x(0) — x(2 \pi) = x’(0) —x’(2 \pi) = 0$$ under some non-resonance conditions on the asymptotic behavior of $x^{-1}g(t, x)$ for $|x| \to \infty$.
General
33
42
10.4171/ZAA/88a
http://www.ems-ph.org/doi/10.4171/ZAA/88a
Eine Realisierung der Theorie der abstrakten Besov-Räume $B_q^s(A) (s > 0, 1 \leq q \leq \infty$) und der Lebesgue-Räume $H^s_{p, \mu}$ auf der Grundlage Besselscher Differentialoperatoren
Gerd
Altenburg
Friedrich-Schiller-Universität Jena, JENA, GERMANY
The paper deals with the theory of abstract Besov-spaces, defined by H. Triebel, in the concrete case of weighted $L_p$-spaces on the base of Bessel-type differential operators. Also spaces of Lebesgue-type on the same base are defined and treated here. Furthermore interpolation theorems are given.
General
43
63
10.4171/ZAA/89
http://www.ems-ph.org/doi/10.4171/ZAA/89
Necessary optimality conditions for systems described by nonlinear elliptic equations. I (in Russian)
Uldis
Raitums
University of Latvia, RIGA, LATVIA
This paper considers optimal control problems for systems governed by second order elliptic differential equations in divergence form with nonlinear terms and control appear in all terms. The representation of the main part of increment for a solution of the state equation is given in the case of needle-like variations.
General
65
79
10.4171/ZAA/90
http://www.ems-ph.org/doi/10.4171/ZAA/90
On the existence of the solution of an abstract optimization problem related to a quasi-variational inequality
Gottfried
Bruckner
Karl-Weierstraß-Institut für Mathematik, BERLIN, GERMANY
A general concept is given to get existence and regularity results for an optimization problem that is closely connected to a quasi-variational inequality.
General
81
86
10.4171/ZAA/91
http://www.ems-ph.org/doi/10.4171/ZAA/91
Estimates by Lozinsky’s functional improved in the linear autonomous case
Barnabas
Garay
Technical University of Budapest, BUDAPEST, HUNGARY
Viktor
Kertész
Technical University of Budapest, BUDAPEST, HUNGARY
Using a real-valued functional (denoted by $\mu$) introduced by Lozinsky and defined on matrices, lower and upper bounds can be given for the norm of solutions of linear differential equations. This functional also depends on the norm applied. It is pointed out that the best possible bounds can be obtained applying an appropriate linear transformation of the differential equation. In the real and autonomous case this appropriate linear transformation is real and does not depend on the time if $\mu$ is induced by the Euclidean norm. Moreover, close correspondence between $\mu$ and quadratic Liapunov functions is shown. It is proved that in the general case (not Euclidean norms) the best possible bounds can, generally, not be obtained if the linear transformation does not depend on the time.
General
87
95
10.4171/ZAA/92
http://www.ems-ph.org/doi/10.4171/ZAA/92