Periodic solutions of \(p\)-Laplacian equations via rotation numbers
type: Item
instance of: scholarly article
title: Periodic solutions of \(p\)-Laplacian equations via rotation numbers
zbMATH Open document ID: 1471.34081
author: Shuang Wang
author: Dingbian Qian
published in: Communications on Pure and Applied Analysis
publication date: 2021-06-16T00:00:00Z
review text: The authors prove existence and multiplicity results for periodic solutions of the \(p\)-Laplacian equation \[ (|x'|^{p-2}x')' + f(t,x) = 0. \] Both asymptotically linear and superlinear nonlinearities are studied, in absence of global existence and uniqueness conditions on the solutions of the associated Cauchy problems. Some classical results for second order differential equations (i.e., the case \(p=2\)) are thus extended. The proofs make use of a recent version of the Poincaré-Birkhoff theorem provided by Fonda and Ureña.
reviewed by: Alessandro Fonda
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7359982
zbMATH Keywords: periodic solutions
zbMATH Keywords: \(p\)-Laplacian equation
zbMATH Keywords: rotation number, Poincaré-Birkhoff theorem
MaRDI profile type: Publication
full work available at URL: cpaa.2021060
OpenAlex ID: W3141458607
cites work: Generalization of Fredholm alternative for nonlinear differential operators
cites work: Existence of multiplicity harmonic and subharmonic solutions for second-order quasilinear equation via Poincaré-Birkhoff twist theorem
cites work: A variational approach to nonresonance with respect to the Fučik spectrum
cites work: Multiplicity results for asymptotically linear equations, using the rotation number approach
cites work: A Generalization of the Poincare-Birkhoff Theorem
cites work: Periodic solutions of Duffing's equations with superquadratic potential
cites work: Periodic solutions of weakly coupled superlinear systems
cites work: A higher dimensional Poincaré-Birkhoff theorem for Hamiltonian flows
cites work: Generalizations of the Poincaré-Birkhoff theorem
cites work: A Fredholm-like result for strongly nonlinear second order ODE's
cites work: On boundary value problems for superlinear second order differential equations
cites work: Periodic solutions of x''+f(x,t)=0 via the Poincaré-Birkhoff theorem
cites work: Periodic solution for nonlinear systems with \(p\)-Laplacian-like operators
cites work: Time-mappings and multiplicity of solutions for the one-dimensional p-Laplacian
cites work: On the use of Morse index and rotation numbers for multiplicity results of resonant BVPs
cites work: Periodic solutions for the 1-dimensional \(p\)-Laplacian equation
cites work: A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
cites work: Existence and multiplicity of solutions with prescribed period for a second order quasilinear O.D.E.
cites work: Infinitely many \(T\)-periodic solutions for a problem arising in nonlinear elasticity
cites work: Infinity of subharmonics for asymmetric Duffing equations with the Lazer-Leach-Dancer condition
cites work: Periodic Motions of Linear Impact Oscillators via the Successor Map
cites work: Periodic solutions of superlinear impulsive differential equations: a geometric approach
cites work: Periodic solutions of second order equations via rotation numbers
cites work: A note on the Poincaré—Birkhoff fixed point theorem and periodic solutions of planar systems
cites work: Q5297301
cites work: ROTATION NUMBER, PERIODIC FUČIK SPECTRUM AND MULTIPLE PERIODIC SOLUTIONS
cites work: Nonuniform nonresonance at the first eigenvalue of the p-laplacian
cites work: Nonuniform nonresonance of semilinear differential equations
DOI: 10.3934/CPAA.2021060
description: scientific article; zbMATH DE number 7359982