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Displaying similar documents to “Periodic boundary value problem of a fourth order differential inclusion”

Selivanovski hard sets are hard

Janusz Pawlikowski (2015)

Fundamenta Mathematicae

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Let H Z 2 ω . For n ≥ 2, we prove that if Selivanovski measurable functions from 2 ω to Z give as preimages of H all Σₙ¹ subsets of 2 ω , then so do continuous injections.

On boundary value problems for systems of nonlinear generalized ordinary differential equations

Malkhaz Ashordia (2017)

Czechoslovak Mathematical Journal

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A general theorem (principle of a priori boundedness) on solvability of the boundary value problem d x = d A ( t ) · f ( t , x ) , h ( x ) = 0 is established, where f : [ a , b ] × n n is a vector-function belonging to the Carathéodory class corresponding to the matrix-function A : [ a , b ] n × n with bounded total variation components, and h : BV s ( [ a , b ] , n ) n is a continuous operator. Basing on the mentioned principle of a priori boundedness, effective criteria are obtained for the solvability of the system under the condition x ( t 1 ( x ) ) = ( x ) · x ( t 2 ( x ) ) + c 0 , where t i : BV s ( [ a , b ] , n ) [ a , b ] ( i = 1 , 2 ) and : BV s ( [ a , b ] , n ) n are continuous...

Some properties of algebras of real-valued measurable functions

Ali Akbar Estaji, Ahmad Mahmoudi Darghadam (2023)

Archivum Mathematicum

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Let M ( X , 𝒜 ) ( M * ( X , 𝒜 ) ) be the f -ring of all (bounded) real-measurable functions on a T -measurable space ( X , 𝒜 ) , let M K ( X , 𝒜 ) be the family of all f M ( X , 𝒜 ) such that coz ( f ) is compact, and let M ( X , 𝒜 ) be all f M ( X , 𝒜 ) that { x X : | f ( x ) | 1 n } is compact for any n . We introduce realcompact subrings of M ( X , 𝒜 ) , we show that M * ( X , 𝒜 ) is a realcompact subring of M ( X , 𝒜 ) , and also M ( X , 𝒜 ) is a realcompact if and only if ( X , 𝒜 ) is a compact measurable space. For every nonzero real Riesz map ϕ : M ( X , 𝒜 ) , we prove that there is an element x 0 X such that ϕ ( f ) = f ( x 0 ) for every f M ( X , 𝒜 ) if ( X , 𝒜 ) is a compact measurable space....

L₁-uniqueness of degenerate elliptic operators

Derek W. Robinson, Adam Sikora (2011)

Studia Mathematica

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Let Ω be an open subset of d with 0 ∈ Ω. Furthermore, let H Ω = - i , j = 1 d i c i j j be a second-order partial differential operator with domain C c ( Ω ) where the coefficients c i j W l o c 1 , ( Ω ̅ ) are real, c i j = c j i and the coefficient matrix C = ( c i j ) satisfies bounds 0 < C(x) ≤ c(|x|)I for all x ∈ Ω. If 0 d s s d / 2 e - λ μ ( s ) ² < for some λ > 0 where μ ( s ) = 0 s d t c ( t ) - 1 / 2 then we establish that H Ω is L₁-unique, i.e. it has a unique L₁-extension which generates a continuous semigroup, if and only if it is Markov unique, i.e. it has a unique L₂-extension which generates a submarkovian semigroup....

Cobham's theorem for substitutions

Fabien Durand (2011)

Journal of the European Mathematical Society

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The seminal theorem of Cobham has given rise during the last 40 years to a lot of work about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let α and β be two multiplicatively independent Perron numbers. Then a sequence x A , where A is a finite alphabet, is both α -substitutive and β -substitutive if and only if x is ultimately...

Some theorems of Korovkin type

Tomoko Hachiro, Takateru Okayasu (2003)

Studia Mathematica

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We take another approach to the well known theorem of Korovkin, in the following situation: X, Y are compact Hausdorff spaces, M is a unital subspace of the Banach space C(X) (respectively, C ( X ) ) of all complex-valued (resp., real-valued) continuous functions on X, S ⊂ M a complex (resp., real) function space on X, ϕₙ a sequence of unital linear contractions from M into C(Y) (resp., C ( Y ) ), and ϕ a linear isometry from M into C(Y) (resp., C ( Y ) ). We show, under the assumption that Π N Π T , where Π N is...

Existence of positive solutions for second order m-point boundary value problems

Ruyun Ma (2002)

Annales Polonici Mathematici

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Let α,β,γ,δ ≥ 0 and ϱ:= γβ + αγ + αδ > 0. Let ψ(t) = β + αt, ϕ(t) = γ + δ - γt, t ∈ [0,1]. We study the existence of positive solutions for the m-point boundary value problem ⎧u” + h(t)f(u) = 0, 0 < t < 1, ⎨ α u ( 0 ) - β u ' ( 0 ) = i = 1 m - 2 a i u ( ξ i ) γ u ( 1 ) + δ u ' ( 1 ) = i = 1 m - 2 b i u ( ξ i ) , where ξ i ( 0 , 1 ) , a i , b i ( 0 , ) (for i ∈ 1,…,m-2) are given constants satisfying ϱ - i = 1 m - 2 a i ϕ ( ξ i ) > 0 , ϱ - i = 1 m - 2 b i ψ ( ξ i ) > 0 and Δ : = - i = 1 m - 2 a i ψ ( ξ i ) ϱ - i = 1 m - 2 a i ϕ ( ξ i ) ϱ - i = 1 m - 2 b i ψ ( ξ i ) - i = 1 m - 2 b i ϕ ( ξ i ) < 0 . We show the existence of positive solutions if f is either superlinear or sublinear by a simple application of a fixed point theorem in cones. Our result extends a result established by Erbe and...

On the uniqueness of periodic decomposition

Viktor Harangi (2011)

Fundamenta Mathematicae

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Let a , . . . , a k be arbitrary nonzero real numbers. An ( a , . . . , a k ) -decomposition of a function f:ℝ → ℝ is a sum f + + f k = f where f i : is an a i -periodic function. Such a decomposition is not unique because there are several solutions of the equation h + + h k = 0 with h i : a i -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the ( a , . . . , a k ) -decomposition is essentially unique. We characterize those periods for which essential...

A symmetry problem in the calculus of variations

Graziano Crasta (2006)

Journal of the European Mathematical Society

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We consider the integral functional J ( u ) = Ω [ f ( | D u | ) u ] d x , u W 0 1 , 1 ( Ω ) , where Ω n , n 2 , is a nonempty bounded connected open subset of n with smooth boundary, and s f ( | s | ) is a convex, differentiable function. We prove that if J admits a minimizer in W 0 1 , 1 ( Ω ) depending only on the distance from the boundary of Ω , then Ω must be a ball.

Existence theorems for nonlinear differential equations having trichotomy in Banach spaces

Adel Mahmoud Gomaa (2017)

Czechoslovak Mathematical Journal

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We give existence theorems for weak and strong solutions with trichotomy of the nonlinear differential equation x ˙ ( t ) = ( t ) x ( t ) + f ( t , x ( t ) ) , t ( P ) where { ( t ) : t } is a family of linear operators from a Banach space E into itself and f : × E E . By L ( E ) we denote the space of linear operators from E into itself. Furthermore, for a < b and d > 0 , we let C ( [ - d , 0 ] , E ) be the Banach space of continuous functions from [ - d , 0 ] into E and f d : [ a , b ] × C ( [ - d , 0 ] , E ) E . Let ^ : [ a , b ] L ( E ) be a strongly measurable and Bochner integrable operator on [ a , b ] and for t [ a , b ] define τ t x ( s ) = x ( t + s ) for each s [ - d , 0 ] . We prove that, under certain...

Numerical approximation of the non-linear fourth-order boundary-value problem

Svobodová, Ivona

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We consider functionals of a potential energy ψ ( u ) corresponding to 𝑎𝑛 𝑎𝑥𝑖𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 - 𝑣𝑎𝑙𝑢𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚 . We are dealing with 𝑎 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎 𝑡ℎ𝑖𝑛 𝑎𝑛𝑛𝑢𝑙𝑎𝑟 𝑝𝑙𝑎𝑡𝑒 with 𝑁𝑒𝑢𝑚𝑎𝑛𝑛 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 . Various types of the subsoil of the plate are described by various types of the 𝑛𝑜𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑏𝑙𝑒 nonlinear term ψ ( u ) . The aim of the paper is to find a suitable computational algorithm.