- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 15:01:11
9
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PM&vol=66&iss=1&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)
66
2009
1
Existence and uniqueness of periodic solutions for a delay differential equation with piecewise constant arguments
Haihua
Liang
Guangdong Polytechnic Normal University, GUANGZHOU, GUANGDONG, CHINA
Gen-Qiang
Wang
Guangdong Polytechnic Normal University, GUANGZHOU, GUANGDONG, CHINA
First order differential equation with piecewise constant arguments, periodic solutions, existence and uniqueness
We establish existence and uniqueness criteria for the periodic solutions of a first order differential equation with piecewise constant arguments.
Ordinary differential equations
General
1
12
10.4171/PM/1827
http://www.ems-ph.org/doi/10.4171/PM/1827
Existence of solutions for a third-order boundary value problem with p-Laplacian operator and nonlinear boundary conditions
De-Xiang
Ma
North China Electric Power University, Beijing, CHINA
Shu-Zhen
Sun
North China Electric Power University, Beijing, CHINA
Third-order nonlinear boundary condition, Nagumo condition, Schauder fixed point theorem
In this paper we study the third-order nonlinear boundary value problem (Φ(u''))'(t) + f(t, u(t), u'(t), u''(t)) = 0 a.e. t ∈ [0,1], u(0) = 0, g(u'(0), u''(0)) = A, h(u'(1), u''(1)) = B, where A, B ∈ ℝ, f : [0,1] × ℝ3 → ℝ is a Carathéodory function, g, h ∈ C0(ℝ2,ℝ) and Φ ∈ C0(ℝ, ℝ). Using apriori estimates, the Nagumo condition, upper and lower solutions and the Schauder fixed point theorem, we are able to prove existence of solutions of this problem.
Ordinary differential equations
General
13
27
10.4171/PM/1828
http://www.ems-ph.org/doi/10.4171/PM/1828
Existence of a renormalized solution for a class of nonlinear parabolic equations in Orlicz spaces
Elhoussine
Azroul
Université Sidi Mohamed Ben Abdellah, Fès, MOROCCO
Hicham
Redwane
Université Hassan 1, SETTAT, MOROCCO
Mohamed
Rhoudaf
Université Sidi Mohamed Ben Abdellah, Fès, MOROCCO
Nonlinear parabolic equations, Orlicz spaces, existence, renormalized solutions
An existence result for a solution of a class of nonlinear parabolic equations in Orlicz spaces is established. The data belongs to L1, no growth assumption is made on the nonlinearities and the N-function does not satisfy the Δ2 condition.
Operator theory
Functional analysis
General
29
63
10.4171/PM/1829
http://www.ems-ph.org/doi/10.4171/PM/1829
A class of integral domains whose integral closures are small submodules of the quotient field
David
Dobbs
University of Tennessee, KNOXVILLE, UNITED STATES
Integral domain, quotient field, small submodule, valuation domain, overring, integrality, maximal ideal, pullback, D + M construction, locally pseudo-valuation domain
Let (V, M) be a valuation domain which is distinct from its quotient field K, and let π: V → V/M be the canonical surjection. Let D be a subring of V/M. It is proved that the pullback R := π− 1(D) has the property that V (and hence each integral overring of R) is a small R-submodule of K. Applications include all classical D + M constructions and locally pseudo-valuation domains.
Commutative rings and algebras
General
65
70
10.4171/PM/1830
http://www.ems-ph.org/doi/10.4171/PM/1830
Stability criteria for certain third order nonlinear delay differential equations
Cemil
Tunç
Yüzüncü Yıl University, VAN, TURKEY
Asymptotic stability, stability criteria, Lyapunov functional, nonlinear delay differential equation of third order
In this paper we study the asymptotic stability of the trivial solution of third order nonlinear delay differential equations of the form x'''(t) + f(x(t), x'(t))x''(t) + g(x(t − r), x'(t − r)) + h(x(t − r)) = 0, where r > 0 is a constant delay. In proving our result we make use of Lyapunov’s second method by constructing a Lyapunov functional.
Ordinary differential equations
General
71
80
10.4171/PM/1831
http://www.ems-ph.org/doi/10.4171/PM/1831
The counting hierarchy in binary notation
Gilda
Ferreira
Universidade Lusófona de Humanidades e Tecnologias, LISBOA, PORTUGAL
Counting hierarchy, bounded arithmetic, complexity theory
We present a new recursion-theoretic characterization of FCH, the hierarchy of counting functions, in binary notation. Afterwards we introduce a theory of bounded arithmetic, TCA, that can be seen as a reformulation, in the binary setting, of Jan Johannsen and Chris Pollett's system D02. Using the previous inductive characterization of FCH, we show that a strategy similar to the one applied to D02 can be used in order to characterize FCH as the class of functions provably total in TCA.
Computer science
Mathematical logic and foundations
General
81
94
10.4171/PM/1832
http://www.ems-ph.org/doi/10.4171/PM/1832
Multilinear functionals of Schatten class type and approximation numbers
Cristiane de Andrade
Mendes
Universidade Federal de Juiz de Fora, JUIZ DE FORA - MG, BRAZIL
Approximation numbers, multilinear mappings, Schatten classes
In this article we investigate the relationship between multilinear functionals of Schatten class type and approximation numbers, and obtain some results that are similar to the those we know in the linear theory.
Functional analysis
General
95
105
10.4171/PM/1833
http://www.ems-ph.org/doi/10.4171/PM/1833
An existence theorem for a perturbed singular elliptic problem
Giovanni
Anello
Università degli Studi di Messina, MESSINA, ITALY
Singular elliptic problems, classical solution, positive solution
We prove the existence of a positive solution for singular elliptic problems of the type − Δu = α(x)u−β + λf(x, u) in Ω, u| ∂Ω = 0, where β is any positive real number.
Ordinary differential equations
General
107
114
10.4171/PM/1834
http://www.ems-ph.org/doi/10.4171/PM/1834
On simple Filippov superalgebras of type B(0, n), II
Alexander
Pojidaev
Siberian Branch of the Russian Academy of Sciences, NOVOSIBIRSK, RUSSIAN FEDERATION
Paulo
Saraiva
Universidade de Coimbra, COIMBRA, PORTUGAL
Filippov superalgebra, n-Lie (super)algebra, (semi)simple (super)algebra, irreducible module over Lie superalgebra
It is proved that there exist no simple finite-dimensional Filippov superalgebras of type B(0, n) over an algebraically closed field of characteristic 0.
Nonassociative rings and algebras
General
115
130
10.4171/PM/1835
http://www.ems-ph.org/doi/10.4171/PM/1835