Existence, regularity and stability properties of periodic solutions of a capillarity equation in the presence of lower and upper solutions
type: Item
instance of: scholarly article
title: Existence, regularity and stability properties of periodic solutions of a capillarity equation in the presence of lower and upper solutions
zbMATH Open document ID: 1279.34054
author: Franco Obersnel
author: Pierpaolo Omari
author: Sabrina Rivetti
published in: Nonlinear Analysis. Real World Applications
publication date: 2012-12-28T00:00:00Z
review text: The authors study the existence of \(T\)-periodic solutions of the capillarity equation \[ -(u'/\sqrt{1+(u')^2})'=f(t,u), \] with \(f\) a Carathéodory function. To this end, they develop the method of lower and upper solutions both in the case in which such functions are well ordered (the lower solution is under the upper one) and in the case in which they can cross. These functions are assumed to be of bounded variation and their definition is in a variational setting. By assuming some monotonicity and regularity conditions on \(f\), it is proved that the solutions of the problem are in \(C^3\). In the last section, some stability properties are deduced.
reviewed by: Alberto Cabada
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 6118822
zbMATH Keywords: quasilinear ordinary differential equation
zbMATH Keywords: prescribed curvature equation
zbMATH Keywords: capillarity equation
zbMATH Keywords: periodic problem
zbMATH Keywords: bounded variation function
zbMATH Keywords: existence
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: regularity
zbMATH Keywords: order stability
zbMATH Keywords: Lyapunov instability
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2012.04.012
OpenAlex ID: W2034828453
cites work: Q3708392
cites work: On reaction processes with saturating diffusion
cites work: Q3334514
cites work: Periodic solutions for nonlinear systems with mean curvature-like operators
cites work: Boundary-value problems with non-surjective \(\varphi\)-Laplacian and one-sided bounded nonlinearity
cites work: Periodic solutions for nonlinear equations with mean curvature-like operators
cites work: Periodic solutions of nonlinear perturbations of \(\phi\)-Laplacians with possibly bounded \(\phi\)
cites work: Multiple periodic solutions of ordinary differential equations with bounded nonlinearities and \(\varphi\)-Laplacian
cites work: Periodic solutions of pendulum-like perturbations of singular and bounded \({\varphi}\)-Laplacians
cites work: MULTIPLE BOUNDED VARIATION SOLUTIONS OF A PERIODICALLY PERTURBED SINE-CURVATURE EQUATION
cites work: The periodic problem for curvature-like equations with asymmetric perturbations
cites work: Existence and multiplicity results for the prescribed mean curvature equation via lower and upper solutions.
cites work: Existence, regularity and boundary behaviour of bounded variation solutions of a one-dimensional capillarity equation
cites work: Q3998030
cites work: The index of Lyapunov stable fixed points in two dimensions
cites work: Dynamics of periodic second-order equations between an ordered pair of lower and upper solutions
cites work: Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
cites work: Relaxation of the non-parametric Plateau problem with an obstacle
cites work: The Euler Equation for Functionals with Linear Growth
cites work: Q4954179
cites work: Classical and non-classical solutions of a prescribed curvature equation
cites work: Q3533405
cites work: Time maps and exact multiplicity results for one-dimensional prescribed mean curvature equations. II
cites work: Steady state solutions of a bi-stable quasi-linear equation with saturating flux
cites work: On a sub-supersolution method for the prescribed mean curvature problem
cites work: Q5588800
cites work: Bounded perturbations of forced harmonic oscillators at resonance
cites work: MULTIPLE POSITIVE SOLUTIONS OF A ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE PROBLEM
cites work: Two-point boundary value problems. Lower and upper solutions
cites work: Q3801969
cites work: Unstable periodic solutions of a parabolic problem in the presence of non-well-ordered lower and upper solutions
DOI: 10.1016/J.NONRWA.2012.04.012
description: scientific article; zbMATH DE number 6118822