Related papers: Symbolic dynamics for the $N$-centre problem at ne…

It is well known that a single nonlinear fractional Schr\"odinger equation with a potential $V(x)$ and a small parameter $\varepsilon $ may have a positive solution that is concentrated at the nondegenerate minimum point of $V(x)$. In this…

This paper examines impulsive non-autonomous systems with grazing periodic solutions. Surfaces of discontinuity and impact functions of the systems are not depending on the time variable. That is, we can say that the impact conditions are…

This paper establishes an existence theory for distributed periodic solutions to Newton's equation with stochastic time-periodic forcing, where the friction matrix is the Hessian of a twice continuously differentiable friction function.…

We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value…

We are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent $1 < m < \infty$. We first prove the existence of possibly infinitely many…

We propose a mechanism for solving the `negative sign problem'---the inability to assign non-negative weights to quantum Monte Carlo configurations---for a toy model consisting of a frustrated triplet of spin-$1/2$ particles interacting…

In the Newtonian $n$-body problem for solutions with arbitrary energy, which start and end either at a total collision or a parabolic/hyperbolic infinity, we prove some basic results about their Morse and Maslov indices. Moreover for…

We deal with a mechanism of generating distributional chaos in planar nonautonomous ODEs and try to measure chaosity in terms of topological entropy. It is based on the interplay between simple periodic solutions. We prove the existence of…

We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…

We show that there exist $\mathbb{Z}^{2}$ symbolic systems that are strongly irreducible and have no (fully) periodic points

In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…

This article concerns time-periodic solutions to a two-dimensional Sellers-type energy balance model coupled to the three-dimensional primitive equations via a dynamic boundary condition. It is shown that the underlying equations admit at…

In this paper, we showed that for some given suitable density and pressure, there exist infinitely many compactly supported solutions with prescribed energy profile. The proof is mainly based on the convex integration scheme. We construct…

This paper is concerned with the variational problem for the elastic energy defined on symmetric graphs under the unilateral constraint. Assuming that the obstacle function satisfies the symmetric cone condition, we prove (i) uniqueness of…

Hyperbolic problems can at times be solved employing symbolic arguments. This is especially true for the construction of forward (and backward) fundamental solutions. We formulate a corresponding abstract scheme and illustrate its…

The paper is concerned with positive solutions to problems of the type \begin{equation*} -\Delta_{\mathbb{B}^N} u - \lambda u = a(x) |u|^{p-1}\;u \, + \, f \, \;\;\text{in}\;\mathbb{B}^{N}, \quad u \in H^{1}{(\mathbb{B}^{N})},…

Let $\phi:X\to \mathbb R$ be a continuous potential associated with a symbolic dynamical system $T:X\to X$ over a finite alphabet. Introducing a parameter $\beta>0$ (interpreted as the inverse temperature) we study the regularity of the…

We study the critical Neumann problem \begin{equation*} \begin{cases} -\Delta u = |u|^{2^*-2}u &\text{in }\Sigma_\omega,\\ \quad\frac{\partial u}{\partial\nu}=0 &\text{on }\partial\Sigma_\omega, \end{cases} \end{equation*} in the unbounded…

We consider two linearly coupled masses, where one mass can have inelastic impacts with a fixed, rigid stop. This leads to the study of a two degree of freedom, piecewise linear, frictionless, unforced, constrained mechanical system. The…

We give a sufficient condition for systems with symmetries to have periodic solutions with equal periods. We show that the main result can be applied both to Hamiltonian and to non-Hamiltonian systems. We apply the main results to produce…