Nontrivial homoclinic solutions for prescribed mean curvature Rayleigh equations
type: Item
instance of: scholarly article
title: Nontrivial homoclinic solutions for prescribed mean curvature Rayleigh equations
zbMATH Open document ID: 1347.34072
author: Meilin Zheng
author: Jin Li
published in: Advances in Difference Equations
publication date: 2016-09-05T00:00:00Z
review text: The authors establish sufficient conditions on the existence of periodic solutions and homoclinic (to \(0\)) solutions for the equation \[ \Biggl(\frac{x'(t)}{\sqrt{1+{x'(t)}^2}}\Biggr)' + f(x'(t)) + g(x(t)) = e(t), \] where \(f,g,e\) are continuous functions, \(f(0)=g(0)=0\).
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6622906
zbMATH Keywords: prescribed mean curvature Rayleigh equation
zbMATH Keywords: homoclinic solution
zbMATH Keywords: periodic solution
zbMATH Keywords: Mawhin's continuation theorem
reviewed by: Alexey O. Remizov
MaRDI profile type: Publication
full work available at URL: s13662-015-0417-7
OpenAlex ID: W2113762563
Wikidata QID: Q59435766
cites work: On the Dirichlet problem for the prescribed mean curvature equation over general domains
cites work: Heat flow for the equation of surfaces with prescribed mean curvature
cites work: Periodic solutions for nonlinear systems with mean curvature-like operators
cites work: Periodic solutions for nonlinear equations with mean curvature-like operators
cites work: Exact number of solutions of a prescribed mean curvature equation
cites work: One-dimensional prescribed mean curvature equation with exponential nonlinearity
cites work: Time maps and exact multiplicity results for one-dimensional prescribed mean curvature equations. II
cites work: The prescribed mean curvature equation for nonparametric surfaces
cites work: Classical and non-classical solutions of a prescribed curvature equation
cites work: Periodic solutions for prescribed mean curvature Liénard equation with a deviating argument
cites work: Existence of positive solutions of one-dimensional prescribed mean curvature equation
cites work: Periodic solutions for a prescribed mean curvature equation with multiple delays
cites work: Periodic solutions for prescribed mean curvature Rayleigh equation with a deviating argument
cites work: Existence and uniqueness of anti-periodic solutions for prescribed mean curvature Rayleigh equations
cites work: Homoclinic solutions for a kind of prescribed mean curvature Duffing-type equation
cites work: Erratum: ``Existence and uniqueness of anti-periodic solutions for prescribed mean curvature Rayleigh equations''
cites work: Homoclinic solutions for a class of second order neutral functional differential systems
cites work: Homoclinic solutions for a class of second-order \(p\)-Laplacian differential systems with delay
cites work: Existence of homoclinic solutions for a class of neutral functional differential equations
cites work: Homoclinic solutions for a second-order \(p\)-Laplacian functional differential system with local condition
cites work: Coincidence degree, and nonlinear differential equations
cites work: Homoclinic solutions for ordinary \(p\)-Laplacian systems with a coercive potential
DOI: 10.1186/S13662-015-0417-7
Recommended article: HOMOCLINIC SOLUTIONS FOR A PRESCRIBED MEAN CURVATURE RAYLEIGH p-LAPLACIAN EQUATION WITH A DEVIATING ARGUMENT
Recommended article: Homoclinic solutions for a class of prescribed mean curvature Liénard equations
Recommended article: Existence and uniqueness of anti-periodic solutions for prescribed mean curvature Rayleigh equations
Recommended article: Homoclinic solutions for Rayleigh type \(p\)-Laplacian equations with a deviating argument
Recommended article: Homoclinic solutions for \(n\)-dimensional prescribed mean curvature \(p\)-Laplacian equations
Recommended article: Periodic solutions for prescribed mean curvature Rayleigh equations with a deviating argument
Recommended article: Periodic solutions for prescribed mean curvature Rayleigh equation with a deviating argument
Recommended article: Q5498087
Recommended article: Existence of heteroclinic solutions for the prescribed curvature equation
Recommended article: Homoclinic solutions of discrete prescribed mean curvature equations with mixed nonlinearities
description: scientific article; zbMATH DE number 6622906