Existence of periodic solution for a class of beam equation via variational methods
type: Item
instance of: scholarly article
title: Existence of periodic solution for a class of beam equation via variational methods
zbMATH Open document ID: 1492.35017
author: Bruno S. V. de Araújo
author: Claudianor O. Alves
author: Alânnio B. Nobrega
published in: Monatshefte für Mathematik
publication date: 2022-03-21T00:00:00Z
review text: The paper is concerned with a class of beam equations, or generalized membrane equations, of the form \begin{align*} &u_{tt}+\Delta_x^2 u = f(x,t,u),\quad &&\text{in }Q=\Omega\times\mathbb{R},\\ &u(x,t) = D_{ii}u(x,t) = 0 &&\text{on }\partial\Omega,\\ &u(x,t) = u(x,t+2\pi) &&\text{in }Q, \end{align*} where \(\Omega=(0,2\pi)^N\) and \(f\in C^1(Q\times\mathbb{R}^2;\mathbb{R})\) is \(2\pi\)-periodic in \(t\), superlinear in \(u\). Under various growth conditions on the nonlinearity, the authors obtain the existence of a ground state, and more generally, the existence of a nontrivial solution.
reviewed by: Thomas J. Bartsch
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35L35
Mathematics Subject Classification ID: 35L76
zbMATH DE Number: 7493669
zbMATH Keywords: hyperbolic equations
zbMATH Keywords: periodic solutions
zbMATH Keywords: variational methods
zbMATH Keywords: existence of a ground state
MaRDI profile type: Publication
full work available at URL: s00605-021-01583-z
OpenAlex ID: W3184940187
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DOI: 10.1007/S00605-021-01583-Z
description: scientific article; zbMATH DE number 7493669