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In this paper, we study the global existence and regularity of H\"older continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.

Analysis of PDEs · Mathematics 2014-09-17 Geng Chen , Yannan Shen

This paper is concerned with a one dimensional (1D) derivative nonlinear Schr\"odinger equation with periodic boundary conditions \begin{equation*} \mi u_t+u_{xx}+\mi |u|^2u_x=0, \ \ x\in \mathbb{T}:=\mathbb{R}/2\pi\mathbb{Z}.…

Dynamical Systems · Mathematics 2015-04-09 Jie Liu

In this paper, by studying a class of 1-D Sturm-Liouville problems with periodic coefficients, we show and classify the solutions of periodic Schrodinger equations in a multidimensional case, which tells that not all the solutions are Bloch…

Mathematical Physics · Physics 2024-06-27 Yan Li , Bin Yang , Aihui Zhou

We prove the existence of infinitely many classical periodic solutions for a class of semilinear wave equations with periodic boundary conditions. Our argument relies on some new estimates for the linear problem with periodic boundary…

Analysis of PDEs · Mathematics 2011-04-07 Jean Marcel Fokam

We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…

Classical Analysis and ODEs · Mathematics 2024-07-16 Luis Carretero , José Valero

This paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of…

Dynamical Systems · Mathematics 2024-06-19 Hui Wei , Shuguan Ji

We show that a problem on minimal periods of solutions of Lipschitz functional differential equations is closely related to the unique solvability of the periodic problem for linear functional differential equations. Sharp bounds for…

Classical Analysis and ODEs · Mathematics 2013-05-06 E. Bravyi

In this paper, we study the existence of random periodic solutions for semilinear stochastic partial differential equations with multiplicative linear noise on a bounded open domain ${\cal O}\subset {\mathbb R}^d$ with smooth boundary. We…

Probability · Mathematics 2018-03-02 Chunrong Feng , Yue Wu , Huaizhong Zhao

Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…

Classical Analysis and ODEs · Mathematics 2009-04-20 M. A. M. Alwash

We present a set of smooth infinite energy global solutions (without spatial symmetry) to the non-integrable, nonlinear Schr\"odinger equations on $\Bbb R$. These solutions are space-time quasi-periodic with two frequencies each. Previous…

Analysis of PDEs · Mathematics 2021-10-29 W. -M. Wang

We prove existence of infinitely many classical periodic solutions with periodic boundary conditions for a class of monotone semilinear wave equations. Our argument relies on some new estimates for the linear problem with periodic boundary…

Analysis of PDEs · Mathematics 2010-08-27 Jean Marcel Fokam

In this paper, we give a proof of the existence of stationary dark soliton solutions or heteroclinic orbits of nonlinear equations of Schr\"odinger type with periodic inhomogeneous nonlinearity. The result is illustrated with examples of…

Pattern Formation and Solitons · Physics 2015-05-20 J. Belmonte-Beitia , J. Cuevas

We prove the existence of infinitely many nontrivial weak periodic solutions for a class of fractional Kirchhoff problems driven by a relativistic Schr\"odinger operator with periodic boundary conditions and involving different types of…

Analysis of PDEs · Mathematics 2019-07-02 Vincenzo Ambrosio

An explicit lifespan estimate is presented for the derivative Schr\"odinger equations with periodic boundary condition.

Analysis of PDEs · Mathematics 2018-06-06 Kazumasa Fujiwara , Tohru Ozawa

We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case…

Functional Analysis · Mathematics 2007-05-23 Massimiliano Berti , Michela Procesi

In this work we study the existence of periodic and asymptotically periodic solutions of a system of nonlinear Volterra difference equations with infinite delay. By means of fixed point theory, we furnish conditions that guarantee the…

Classical Analysis and ODEs · Mathematics 2013-03-28 Murat Adıvar , H. Can Koyuncuoğlu , Youssef N. Raffoul

Original abstract: "We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions…

General Relativity and Quantum Cosmology · Physics 2023-04-25 Piotr T. Chruściel

In this work we provide conditions for the existence of periodic solutions to nonlinear, second-order difference equations of the form \begin{equation*} y(t+2)+by(t+1)+cy(t)=g(t,y(t)) \end{equation*} where $c\neq 0$, and…

Classical Analysis and ODEs · Mathematics 2015-11-13 Daniel Maroncelli , Jesus Rodriguez

Existence and bifurcation results are derived for quasi periodic traveling waves of discrete nonlinear Schrodinger equations with nonlocal interactions and with polynomial type potentials. Variational tools are used. Several concrete…

Pattern Formation and Solitons · Physics 2009-09-11 Michal Feckan , Vassilis Rothos

In this paper we consider a class of nonlinear wave equation with $x$-dependent coefficients and prove existence of families of time-periodic solutions under the general boundary conditions. Such a model arises from the forced vibrations of…

Dynamical Systems · Mathematics 2017-06-14 Bochao Chen , Yong Li , Xue Yang