- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 13:48:33
7
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=ZAA&vol=37&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)
37
2018
1
Propagation of Regularity and Positive Definiteness: a Constructive Approach
Jorge
Buescu
Universidade de Lisboa, Portugal
António
Paixão
Instituto Superior de Engenharia de Lisboa, Portugal
Claudemir
Oliveira
Universidade Federal de Itajubá, Brazil
Positive definite kernels, positive definite functions, differentiability, holomorphy, constructive approximation, exponentially convex functions
We show that, for positive definite kernels, if specific forms of regularity (continuity, $\mathcal{S}_n$-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole domain of positive-definiteness. This local-to-global propagation of regularity is constructively shown to be a consequence of the algebraic structure induced by the non-negativity of the associated bilinear forms up to order~5. Consequences of these results for topological groups and for positive definite and exponentially convex functions are explored.
Fourier analysis
Real functions
Functions of a complex variable
1
24
10.4171/ZAA/1599
http://www.ems-ph.org/doi/10.4171/ZAA/1599
1
8
2018
On the Robin Problem with Indefinite Weight in Sobolev Spaces with Variable Exponents
Khaled
Kefi
Université de Tunis, Tunisia
Robin problem, Ekeland's variational principle, generalized Sobolev spaces, weak solution
The present paper is concerned with a Robin problem involving an indefinite weight in Sobolev spaces with variable exponents \begin{equation*} \left\{\begin{alignedat}{2}-\text{ div}(|\nabla u|^{p(x)-2}\nabla u)&=\lambda V(x)|u|^{q(x)-2}u,& \quad x&\in\Omega\\ |\nabla u|^{p(x)-2} \frac{\partial u}{\partial n}+a(x)|u|^{p(x)-2}u&=0.&\quad x&\in\partial\Omega \end{alignedat}\right. \end{equation*} By means of the variational approach and Ekeland's principle, we establish that the above problem admits a non-trivial weak solution under appropriate conditions.
Partial differential equations
Functional analysis
25
38
10.4171/ZAA/1600
http://www.ems-ph.org/doi/10.4171/ZAA/1600
1
8
2018
Infinitely many Solutions for Klein–Gordon–Maxwell System with Potentials Vanishing at Infinity
Shang-Jie
Chen
Chongqing Technology and Business University, China
Lin
Li
Chongqing Technology and Business University, China
Klein–Gordon–Maxwell system, variational methods, Fountain Theorem
In this paper, a nonlinear Klein–Gordon–Maxwell system with solitary waves solution is considered. Using critical point theory, we establish sufficient conditions for the existence of Infinitely many radial solitary waves solutions.
Partial differential equations
39
50
10.4171/ZAA/1601
http://www.ems-ph.org/doi/10.4171/ZAA/1601
1
8
2018
Planar Traveling Waves of Mono-Stable Reaction-Diffusion Equations
Xiaohuan
Wang
Henan University, Kaifeng, China
Planar traveling wavefronts, stability, super-solution and sub-solutions, mono-stable reaction-diffusion equations
This paper is concerned with planar traveling wavefronts of mono-stable reaction-diffusion equations in $\mathbb{R}^n$ ($n\geq2$). We show that the large time behavior of the disturbed fronts can be controlled by two functions, which are the solutions of the specified nonlinear parabolic equations in $\mathbb{R}^{n-1}$, and the planar traveling fronts are asymptotically stable in $L^\infty(\mathbb{R}^n)$ under ergodic perturbations, which include quasi-periodic and almost periodic ones as special cases.
Partial differential equations
51
72
10.4171/ZAA/1602
http://www.ems-ph.org/doi/10.4171/ZAA/1602
1
8
2018
Global Well-Posedness for the Gross–Pitaevskii Equation with Pumping and Nonlinear Damping
Binhua
Feng
Northwest Normal University, Lanzhou, Gansu, China
Xiangxia
Yuan
Northwest Normal University, Lanzhou, Gansu, China
Jun
Zheng
Southwest Jiatong University, Emeishan, Sichuan, China
Gross-Pitaevskii equation, global existence, nonlinear damping, pumping
This paper deals with the Cauchy problem for the Gross{Pitaevskii equation with pumping and nonlinear damping which describes the dynamics of pumped decaying Bose–Einstein condensates. This paper establishes global existence of solutions for general initial data in the energy space.
Partial differential equations
73
82
10.4171/ZAA/1603
http://www.ems-ph.org/doi/10.4171/ZAA/1603
1
8
2018
Stability of Global Bounded Solutions to a Nonautonomous Nonlinear Second Order Integro-Differential Equation
Hassan
Yassine
Lebanese University, Zahleh, Lebanon
Evolutionary integral equation, semilinear, stabilization, Lojasiewicz-Simon inequality.
We study the long-time behavior as time goes to infinity of global bounded weak solutions to the following integro-differential equation $$\ddot u+k*\dot u+\nabla E(u)=g, $$ in finite dimensions, where the nonlinear potential $E$ satisfies the Łojasiewicz inequality near some equilibrium point. Based on an appropriate new Lyapunov function and Łojasiewicz inequality we prove that any global bounded weak solution converges to a steady state. We also obtain the rate of convergence according to the Łojasiewicz exponent and the time-dependent right-hand side $g$.
Integral equations
83
99
10.4171/ZAA/1604
http://www.ems-ph.org/doi/10.4171/ZAA/1604
1
8
2018
A Grobman–Hartman Theorem for Differential Equations with Piecewise Constant Arguments of Mixed Type
Manuel
Pinto
Universidad de Chile, Santiago, Chile
Gonzalo
Robledo
Universidad de Chile, Santiago, Chile
Differential equations, piecewise constants arguments, topological equivalence, exponential dichotomy
We obtain sufficient conditions for the existence of a uniformly and Hölder continuous homeomorphism between the solutions of a linear differential system with piecewise constant argument of generalized type and the solutions of a perturbed family. The main tool is a recently introduced definition of exponential dichotomy.
Ordinary differential equations
Difference and functional equations
101
126
10.4171/ZAA/1605
http://www.ems-ph.org/doi/10.4171/ZAA/1605
1
8
2018