- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 06:47:51
4
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PM&vol=64&iss=3&update_since=2024-03-29
Portugaliae Mathematica
Port. Math.
PM
0032-5155
1662-2758
General
10.4171/PM
http://www.ems-ph.org/doi/10.4171/PM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2008)
64
2007
3
A monotone method for fourth order boundary value problems involving a factorizable linear operator
P.
Habets
Université Catholique de Louvain, LOUVAIN-LA-NEUVE, BELGIUM
Margarita
Ramalho
Faculdade de Ciências da Universidade de Lisboa, LISBOA, PORTUGAL
Beam equation, fourth order boundary value problem, periodic solutions, maximum principle, monotone method, upper and lower solutions
We consider the nonlinear fourth order beam equation $$ u^{\iv}=f(t,u,u''), $$ with boundary conditions corresponding to the periodic or the hinged beam problem. In presence of upper and lower solutions, we consider a monotone method to obtain solutions. The main idea is to write the equation in the form $$ u^{\iv}-cu''+du=g(t,u,u''), $$ where $c$, $d$ are adequate constants, and use maximum principles and a suitable decomposition of the operator appearing in the left-hand side.
Partial differential equations
General
255
279
10.4171/PM/1786
http://www.ems-ph.org/doi/10.4171/PM/1786
Homoclinic solutions of a fourth-order travelling wave ODE
Gheorghe
Moroșanu
Central European University, BUDAPEST, HUNGARY
Diko
Souroujon
Economic University of Varna, VARNA, BULGARIA
Stepan
Tersian
University of Rousse, ROUSSE, BULGARIA
Shooting method, water waves
In this paper we investigate via the shooting method the existence of homoclinic solutions of a fourth-order differential equation arising in the theory of water waves.
Ordinary differential equations
General
281
301
10.4171/PM/1787
http://www.ems-ph.org/doi/10.4171/PM/1787
The Tutte polynomial of a morphism of matroids 4. Computational complexity
Michel
Las Vergnas
Université Pierre et Marie Curie, PARIS CEDEX 05, FRANCE
Matroid, strong map, quotient, matroid perspective, Tutte polynomial, knot polynomial, complexity, easy point, binary
We determine the easy points of the 3-variable Tutte polynomial of a matroid perspective. It turns out that all but one of the sporadic easy points of the 3-variable Tutte polynomial proceed from the 8 sporadic easy points determined in the seminal paper of Jaeger--Vertigan--Welsh on the computational complexity of the Tutte polynomial of a matroid. The exceptional easy point, namely $(-1,-1,-1)$, can be evaluated with polynomial complexity for binary matroid perspectives by a previous result of the author.
Convex and discrete geometry
General
303
309
10.4171/PM/1788
http://www.ems-ph.org/doi/10.4171/PM/1788
Simplicity of Lyapunov spectra: a sufficient criterion
Artur
Avila
Université Pierre et Marie Curie, PARIS CEDEX 05, FRANCE
Marcelo
Viana
, RIO DE JANEIRO, BRAZIL
We exhibit an explicit sufficient condition for the Lyapunov exponents of a linear cocycle over a Markov map to have multiplicity 1. This builds on work of Guivarc'h–Raugi and Gol'dsheid–Margulis, who considered products of random matrices, and of Bonatti–Viana, who dealt with the case when the base dynamics is a subshift of finite type. Here the Markov structure may have infinitely many symbols and the ambient space needs not be compact. As an application, in another paper we prove the Zorich–Kontsevich conjecture on the Lyapunov spectrum of the Teichmüller flow in the space of translation surfaces.
Probability theory and stochastic processes
General
311
376
10.4171/PM/1789
http://www.ems-ph.org/doi/10.4171/PM/1789