Displaying similar documents to “Capacitary strong type estimates in semilinear problems”

Study of Stability in Nonlinear Neutral Differential Equations with Variable Delay Using Krasnoselskii–Burton’s Fixed Point

Mouataz Billah MESMOULI, Abdelouaheb Ardjouni, Ahcene Djoudi (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper, we use a modification of Krasnoselskii’s fixed point theorem introduced by Burton (see [Burton, T. A.: Liapunov functionals, fixed points and stability by Krasnoseskii’s theorem. Nonlinear Stud., 9 (2002), 181–190.] Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equation with variable delay x ' t = - a t h x t + d d t Q t , x t - τ t + G t , x t , x t - τ t . The stability of the zero solution of this eqution provided that h 0 = Q t , 0 = G t , 0 , 0 = 0 . The Caratheodory condition is used for the functions...

Inequalities for the arithmetical functions of Euler and Dedekind

Horst Alzer, Man Kam Kwong (2020)

Czechoslovak Mathematical Journal

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For positive integers n , Euler’s phi function and Dedekind’s psi function are given by φ ( n ) = n p n p prime 1 - 1 p and ψ ( n ) = n p n p prime 1 + 1 p , respectively. We prove that for all n 2 we have 1 - 1 n n - 1 1 + 1 n n + 1 φ ( n ) n φ ( n ) ψ ( n ) n ψ ( n ) and φ ( n ) n ψ ( n ) ψ ( n ) n φ ( n ) 1 - 1 n n + 1 1 + 1 n n - 1 . The sign of equality holds if and only if n is a prime. The first inequality refines results due to Atanassov (2011) and Kannan & Srikanth (2013).

Norm inequalities for the difference between weighted and integral means of operator differentiable functions

Silvestru Sever Dragomir (2020)

Archivum Mathematicum

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Let f be a continuous function on I and A , B 𝒮𝒜 I H , the convex set of selfadjoint operators with spectra in I . If A B and f , as an operator function, is Gateaux differentiable on [ A , B ] : = ( 1 - t ) A + t B t 0 , 1 , while p : 0 , 1 is Lebesgue integrable, then we have the inequalities 0 1 p τ f 1 - τ A + τ B d τ - 0 1 p τ d τ 0 1 f 1 - τ A + τ B d τ 0 1 τ ( 1 - τ ) | τ 1 p s d s 1 - τ - 0 τ p s d s τ | f 1 - τ A + τ B B - A d τ 1 4 0 1 | τ 1 p s d s 1 - τ - 0 τ p s d s τ | f 1 - τ A + τ B B - A d τ , where f is the Gateaux derivative of f .

On motions with bursting characters for Lagrangian mechanical systems with a scalar control. II. A geodesic property of motions with bursting characters for Lagrangian systems

Aldo Bressan, Marco Favretti (1992)

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

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This Note is the continuation of a previous paper with the same title. Here (Part II) we show that for every choice of the sequence u a ( ) , Σ a 's trajectory l a after the instant d + η a tends in a certain natural sense, as a , to a certain geodesic l of V d , with origin at q ¯ , u ¯ . Incidentally l is independent of the choice of applied forces in a neighbourhood of q ¯ , u ¯ arbitrarily prefixed.

Legendre polynomials and supercongruences

Zhi-Hong Sun (2013)

Acta Arithmetica

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Let p > 3 be a prime, and let Rₚ be the set of rational numbers whose denominator is not divisible by p. Let Pₙ(x) be the Legendre polynomials. In this paper we mainly show that for m,n,t ∈ Rₚ with m≢ 0 (mod p), P [ p / 6 ] ( t ) - ( 3 / p ) x = 0 p - 1 ( ( x ³ - 3 x + 2 t ) / p ) ( m o d p ) and ( x = 0 p - 1 ( ( x ³ + m x + n ) / p ) ) ² ( ( - 3 m ) / p ) k = 0 [ p / 6 ] 2 k k 3 k k 6 k 3 k ( ( 4 m ³ + 27 n ² ) / ( 12 ³ · 4 m ³ ) ) k ( m o d p ) , where (a/p) is the Legendre symbol and [x] is the greatest integer function. As an application we solve some conjectures of Z. W. Sun and the author concerning k = 0 p - 1 2 k k 3 k k 6 k 3 k / m k ( m o d p ² ) , where m is an integer not divisible by p.

Boundedness of oriented walks generated by substitutions

F. M. Dekking, Z.-Y. Wen (1996)

Journal de théorie des nombres de Bordeaux

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Let x = x 0 x 1 be a fixed point of a substitution on the alphabet a , b , and let U a = - 1 - 1 0 1 and U b = 1 1 0 1 . We give a complete classification of the substitutions σ : a , b according to whether the sequence of matrices U x 0 U x 1 U x n n = 0 is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.

Generalization of Fueter's result to R n + 1

Tao Qian (1997)

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

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Fueter's result (see [6,8]) on inducing quaternionic regular functions from holomorphic functions of a complex variable is extended to Euclidean spaces R n + 1 . It is then proved to be consistent with M. Sce's generalization for n being odd integers [6].