Discrete & Continuous Dynamical Systems
January 2022 , Volume 42 , Issue 1
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We study a class of critical Kirchhoff problems with a general nonlocal term. The main difficulty here is the absence of a closed-form formula for the compactness threshold. First we obtain a variational characterization of this threshold level. Then we prove a series of existence and multiplicity results based on this variational characterization.
We study the second-order boundary value problem
Consider the second order nonautonomous lattice systemswith singular perturbations
and the first order nonautonomous lattice systems
Under certain conditions, there are pullback attractors
We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions on an evolving domain. Using a Lyapunov functional and duality arguments, we establish the existence of component wise non-negative global solutions.
We consider the following semilinear problem with a gradient term in the nonlinearity
In this paper we establish the existence of at least two (weak) solutions for the following fractional Kirchhoff problem involving singular and exponential nonlinearities
We extend recent orbit counts for finitely generated semigroups acting on
This work establishes the relaxation limit from the bipolar Euler-Poisson system to the bipolar drift-diffusion system, for data so that the latter has a smooth solution. A relative energy identity is developed for the bipolar fluid models, and it is used to show that a dissipative weak solution of the bipolar Euler-Poisson system converges in the high-friction regime to a strong and bounded away from vacuum solution of the bipolar drift-diffusion system.
We study bifurcations in finite-parameter families of vector fields on
In this paper, we construct locally generic
This paper is devoted to an anisotropic curvature flow of the form
In this paper, we prove that every quasiconformal deformation of a subhyperbolic rational map on the boundary of a hyperbolic component
The goal of this paper is the study of the integrability of the geodesic flow on
We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical properties of dynamical systems with some hyperbolicity. As an application we check the conditions for the first return map of a class of multi-dimensional non-Markov, non-conformal intermittent maps.
In this paper we find curves minimizing the elastic energy among curves whose length is fixed and whose ends are pinned. Applying the shooting method, we can identify all critical points explicitly and determine which curve is the global minimizer. As a result we show that the critical points consist of wavelike elasticae and the minimizers do not have any loops or interior inflection points.
In this work, we will introduce a general framework to derive the thermodynamics of a fluid mechanical system, which guarantees the consistence between the energetic variational approaches with the laws of thermodynamics. In particular, we will focus on the coupling between the thermal and mechanical forces. We follow the framework for a classical gas with ideal gas equilibrium and present the existences of weak solutions to this thermodynamic system coupled with the Brinkman-type equation to govern the velocity field.
The exact null-controllability problem in the class of smooth controls with applications to interconnected systems was considered in [
In this paper we show the existence of a nonnegative solution for a singular problem with logarithmic and exponential nonlinearity, namely
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