Displaying similar documents to “On hyperbolic partial differential equations in Banach spaces”

On hyperbolic partial differential equations in Banach spaces

Bogdan Rzepecki (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Viene dimostrata l'esistenza di soluzioni del problema di Darboux per l'equazione iperbolica z x y ′′ = f ( x , y , z , Z x , z y ) sul planiquarto x 0 , y 0 . Qui, f è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza α .

Elementary operators on Banach algebras and Fourier transform

Miloš Arsenović, Dragoljub Kečkić (2006)

Studia Mathematica

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We consider elementary operators x j = 1 n a j x b j , acting on a unital Banach algebra, where a j and b j are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families a j and b j , i.e. a j = a j ' + i a j ' ' ( b j = b j ' + i b j ' ' ), where all a j ' and a j ' ' ( b j ' and b j ' ' ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class...

On the solutions of the inhomogeneous evolution equation in Banach spaces

Eugenio Sinestrari (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Vengono dati nuovi teoremi di regolarità per le soluzioni dell'equazione u ( t ) = Λ u ( t ) + f ( t ) nel caso in cui Λ è il generatore infinitesimale di un semigruppo analitico in uno spazio di Banach E e f è una funzione continua.

Abstract semilinear equations in Banach spaces

Eugenio Sinestrari (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si studiano le proprietà delle soluzioni dell'equazione semilineare astratta u ( t ) = Λ u ( t ) + φ ( t , u ( t ) ) quando Λ è il generatore infinitesimale di un semigruppo analitico in uno spazio di Banach. Vengono provati nuovi teoremi di regolarità anche nel caso in cui φ non è continuo in tutto lo spazio.

A compactness result in thin-film micromagnetics and the optimality of the Néel wall

Radu Ignat, Felix Otto (2008)

Journal of the European Mathematical Society

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In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for S 1 -valued maps m ' (the magnetization) of two variables x ' : E ε ( m ' ) = ε | ' · m ' | 2 d x ' + 1 2 | ' | - 1 / 2 ' · m ' 2 d x ' . We are interested in the behavior of minimizers as ε 0 . They are expected to be S 1 -valued maps m ' of vanishing distributional divergence ' · m ' = 0 , so that appropriate boundary conditions enforce line discontinuities. For finite ε > 0 , these line discontinuities are approximated by smooth transition layers, the so-called Néel...

Boundedness criteria for a class of second order nonlinear differential equations with delay

Daniel O. Adams, Mathew Omonigho Omeike, Idowu A. Osinuga, Biodun S. Badmus (2023)

Mathematica Bohemica

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We consider certain class of second order nonlinear nonautonomous delay differential equations of the form a ( t ) x ' ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) and ( a ( t ) x ' ) ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) , where a , b , c , g , h , m and p are real valued functions which depend at most on the arguments displayed explicitly and r is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski functional to establish our results....

Bigraphic pairs with a realization containing a split bipartite-graph

Jian Hua Yin, Jia-Yun Li, Jin-Zhi Du, Hai-Yan Li (2019)

Czechoslovak Mathematical Journal

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Let K s , t be the complete bipartite graph with partite sets { x 1 , ... , x s } and { y 1 , ... , y t } . A split bipartite-graph on ( s + s ' ) + ( t + t ' ) vertices, denoted by SB s + s ' , t + t ' , is the graph obtained from K s , t by adding s ' + t ' new vertices x s + 1 , ... , x s + s ' , y t + 1 , ... , y t + t ' such that each of x s + 1 , ... , x s + s ' is adjacent to each of y 1 , ... , y t and each of y t + 1 , ... , y t + t ' is adjacent to each of x 1 , ... , x s . Let A and B be nonincreasing lists of nonnegative integers, having lengths m and n , respectively. The pair ( A ; B ) is potentially SB s + s ' , t + t ' -bigraphic if there is a simple bipartite graph containing SB s + s ' , t + t ' (with s + s ' vertices x 1 , ... , x s + s ' in the part of size m ...

E 1 -degeneration and d ' d ' ' -lemma

Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh (2016)

Commentationes Mathematicae Universitatis Carolinae

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For a double complex ( A , d ' , d ' ' ) , we show that if it satisfies the d ' d ' ' -lemma and the spectral sequence { E r p , q } induced by A does not degenerate at E 0 , then it degenerates at E 1 . We apply this result to prove the degeneration at E 1 of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of d ' d ' ' -lemma.

On the solutions of the inhomogeneous evolution equation in Banach spaces

Eugenio Sinestrari (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Vengono dati nuovi teoremi di regolarità per le soluzioni dell'equazione u ( t ) = Λ u ( t ) + f ( t ) nel caso in cui Λ è il generatore infinitesimale di un semigruppo analitico in uno spazio di Banach E e f è una funzione continua.

Duality of matrix-weighted Besov spaces

Svetlana Roudenko (2004)

Studia Mathematica

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We determine the duals of the homogeneous matrix-weighted Besov spaces p α q ( W ) and p α q ( W ) which were previously defined in [5]. If W is a matrix A p weight, then the dual of p α q ( W ) can be identified with p ' - α q ' ( W - p ' / p ) and, similarly, [ p α q ( W ) ] * p ' - α q ' ( W - p ' / p ) . Moreover, for certain W which may not be in the A p class, the duals of p α q ( W ) and p α q ( W ) are determined and expressed in terms of the Besov spaces p ' - α q ' ( A Q - 1 ) and p ' - α q ' ( A Q - 1 ) , which we define in terms of reducing operators A Q Q associated with W. We also develop the basic theory of these reducing operator Besov spaces....

On a divisibility problem

Shichun Yang, Florian Luca, Alain Togbé (2019)

Mathematica Bohemica

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Let p 1 , p 2 , be the sequence of all primes in ascending order. Using explicit estimates from the prime number theory, we show that if k 5 , then ( p k + 1 - 1 ) ! ( 1 2 ( p k + 1 - 1 ) ) ! p k ! , which improves a previous result of the second author.

On Fourier asymptotics of a generalized Cantor measure

Bérenger Akon Kpata, Ibrahim Fofana, Konin Koua (2010)

Colloquium Mathematicae

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Let d be a positive integer and μ a generalized Cantor measure satisfying μ = j = 1 m a j μ S j - 1 , where 0 < a j < 1 , j = 1 m a j = 1 , S j = ρ R + b j with 0 < ρ < 1 and R an orthogonal transformation of d . Then ⎧1 < p ≤ 2 ⇒ ⎨ s u p r > 0 r d ( 1 / α ' - 1 / p ' ) ( J x r | μ ̂ ( y ) | p ' d y ) 1 / p ' D ρ - d / α ' , x d , ⎩ p = 2 ⇒ infr≥1 rd(1/α’-1/2) (∫J₀r|μ̂(y)|² dy)1/2 ≥ D₂ρd/α’ , where J x r = i = 1 d ( x i - r / 2 , x i + r / 2 ) , α’ is defined by ρ d / α ' = ( j = 1 m a j p ) 1 / p and the constants D₁ and D₂ depend only on d and p.

Existence and regularity results for abstract non autonomous parabolic equations

Paolo Acquistapace, Brunello Terreni (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si studiano esistenza, unicità e regolarità delle soluzioni strette, classiche e forti dell’equazione di evoluzione non autonoma u ( t ) A ( t ) u ( t ) = f ( t ) , con il dato iniziale u ( 0 ) = x , in spazi di Banach. I dominii degli operatori A ( t ) variano in t e non sono necessariamente densi in E . Si danno condizioni necessarie e sufficienti per l'esistenza e la regolarità holderiana della soluzione e della sua derivata.

Convolution theorems for starlike and convex functions in the unit disc

M. Anbudurai, R. Parvatham, S. Ponnusamy, V. Singh (2004)

Annales Polonici Mathematici

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Let A denote the space of all analytic functions in the unit disc Δ with the normalization f(0) = f’(0) − 1 = 0. For β < 1, let P β = f A : R e f ' ( z ) > β , z Δ . For λ > 0, suppose that denotes any one of the following classes of functions: M 1 , λ ( 1 ) = f : R e z ( z f ' ( z ) ) ' ' > - λ , z Δ , M 1 , λ ( 2 ) = f : R e z ( z ² f ' ' ( z ) ) ' ' > - λ , z Δ , M 1 , λ ( 3 ) = f : R e 1 / 2 ( z ( z ² f ' ( z ) ) ' ' ) ' - 1 > - λ , z Δ . The main purpose of this paper is to find conditions on λ and γ so that each f ∈ is in γ or γ , γ ∈ [0,1/2]. Here γ and γ respectively denote the class of all starlike functions of order γ and the class of all convex functions of order γ. As a consequence, we obtain...

Existence of solutions for a coupled system with φ -Laplacian operators and nonlinear coupled boundary conditions

Konan Charles Etienne Goli, Assohoun Adjé (2017)

Communications in Mathematics

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We study the existence of solutions of the system ( φ 1 ( u 1 ' ( t ) ) ) ' = f 1 ( t , u 1 ( t ) , u 2 ( t ) , u 1 ' ( t ) , u 2 ' ( t ) ) , a.e. t [ 0 , T ] , ( φ 2 ( u 2 ' ( t ) ) ) ' = f 2 ( t , u 1 ( t ) , u 2 ( t ) , u 1 ' ( t ) , u 2 ' ( t ) ) , a.e. t [ 0 , T ] , submitted to nonlinear coupled boundary conditions on [ 0 , T ] where φ 1 , φ 2 : ( - a , a ) , with 0 < a < + , are two increasing homeomorphisms such that φ 1 ( 0 ) = φ 2 ( 0 ) = 0 , and f i : [ 0 , T ] × 4 , i { 1 , 2 } are two L 1 -Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.

Oscillation criteria for fourth order half-linear differential equations

Jaroslav Jaroš, Kusano Takaŝi, Tomoyuki Tanigawa (2020)

Archivum Mathematicum

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Criteria for oscillatory behavior of solutions of fourth order half-linear differential equations of the form ( | y ' ' | α sgn y ' ' ) ' ' + q ( t ) | y | α sgn y = 0 , t a > 0 , A where α > 0 is a constant and q ( t ) is positive continuous function on [ a , ) , are given in terms of an increasing continuously differentiable function ω ( t ) from [ a , ) to ( 0 , ) which satisfies a 1 / ( t ω ( t ) ) d t < .

On the abstract Cauchy problem in the case of constant domains

Paolo Acquistapace, Brunello Terreni (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si studiano esistenza, unicità e regolarità delle soluzioni strette, classiche e forti u 𝐂 ( [ 0 , T ] , E ) dell'equazione di evoluzione non autonoma u ( t ) - A ( t ) u ( t ) = f ( t ) con il dato iniziale u ( 0 ) = x , in uno spazio di Banach E . Gli operatori A ( t ) sono generatori infinitesimali di semi-gruppi analitici ed hanno dominio indipendente da t e non necessariamente denso in E . Si danno condizioni necessarie e sufficienti per l'esistenza e la regolarità hölderiana della soluzione e della sua derivata.

Couples of lower and upper slopes and resonant second order ordinary differential equations with nonlocal boundary conditions

Jean Mawhin, Katarzyna Szymańska-Dębowska (2016)

Mathematica Bohemica

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A couple ( σ , τ ) of lower and upper slopes for the resonant second order boundary value problem x ' ' = f ( t , x , x ' ) , x ( 0 ) = 0 , x ' ( 1 ) = 0 1 x ' ( s ) d g ( s ) , with g increasing on [ 0 , 1 ] such that 0 1 d g = 1 , is a couple of functions σ , τ C 1 ( [ 0 , 1 ] ) such that σ ( t ) τ ( t ) for all t [ 0 , 1 ] , σ ' ( t ) f ( t , x , σ ( t ) ) , σ ( 1 ) 0 1 σ ( s ) d g ( s ) , τ ' ( t ) f ( t , x , τ ( t ) ) , τ ( 1 ) 0 1 τ ( s ) d g ( s ) , in the stripe 0 t σ ( s ) d s x 0 t τ ( s ) d s and t [ 0 , 1 ] . It is proved that the existence of such a couple ( σ , τ ) implies the existence and localization of a solution to the boundary value problem. Multiplicity results are also obtained.