Related papers: A maximum principle for systems with variational s…

A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or…

This paper is dedicated to the investigation of the asymptotic behavior of a delayed wave equation without the presence of any position term. First, it is shown that the problem is well-posed in the sense of semigroups theory. Thereafter,…

The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at…

We rigorously show that a class of systems of partial differential equations modeling wave bifurcations supports stationary equivariant bifurcation dynamics through deriving its full dynamics on the center manifold(s). A direct consequence…

Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…

A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…

We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first that the problem is well posed. Second, using the LaSalle's…

We establish three variational principles for the upper metric mean dimension with potential of level sets of continuous maps in terms of the entropy of partitions and Katok's entropy of the underlying system. Our results hold for dynamical…

We prove the existence of three-dimensional steady gravity-capillary waves with vorticity on water of finite depth. The waves are periodic with respect to a given two-dimensional lattice and the relative velocity field is a Beltrami field,…

Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These…

Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…

In this work, we consider a system of two wave equations coupled by velocities in one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling…

We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…

In this paper we prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a finite dimensional stochastic differential equation, driven by a multidimensional Wiener process. We drop the usual…

We show the local wellposedness of biharmonic wave maps with initial data of sufficiently high Sobolev regularity and a blow-up criterion in the sup-norm of the gradient of the solutions. In contrast to the wave maps equation we use a…

We investigate standing waves with prescribed mass for a class of Schrodinger equations with competing Van Der Waals type potentials, arising in a model of non-relativistic bosonic atoms and molecules. By developing an approach based on a…

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…

The tadpole graph consists of a circle and a half-line attached at a vertex. We analyze standing waves of the nonlinear Schr\"{o}dinger equation with quintic power nonlinearity equipped with the Neumann-Kirchhoff boundary conditions at the…

In a recent paper (see [7]), a quasi-nonlocal coupling method was introduced to seamlessly bridge a nonlocal diffusion model with the classical local diffusion counterpart in a one-dimensional space. The proposed coupling framework removes…

We consider systems of the form \[ \left\{ \begin{array}{l} -\Delta u + u = \frac{2p}{p+q}(I_\alpha \ast |v|^{q})|u|^{p-2}u \ \ \textrm{ in } \mathbb{R}^N, \\ -\Delta v + v = \frac{2q}{p+q}(I_\alpha \ast |u|^{p})|v|^{q-2}v \ \ \textrm{ in }…