On the non-convergence of successive approximations in the Darboux problem for the equation
M. Kisielewicz (1977)
Colloquium Mathematicae
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M. Kisielewicz (1977)
Colloquium Mathematicae
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Bogdan Rzepecki (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Viene dimostrata l'esistenza di soluzioni del problema di Darboux per l'equazione iperbolica sul planiquarto , . Qui, è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza .
Ján Andres (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi , si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.
Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh (2016)
Commentationes Mathematicae Universitatis Carolinae
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For a double complex , we show that if it satisfies the -lemma and the spectral sequence induced by does not degenerate at , then it degenerates at . We apply this result to prove the degeneration at of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of -lemma.
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 sul planiquarto , . Qui, è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza .
Jean-Marie De Koninck, Imre Kátai (2016)
Colloquium Mathematicae
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We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence is uniformly distributed modulo 1.
Ján Andres (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi , si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.
Yoichi Motohashi (1970)
Acta Arithmetica
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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 -valued maps (the magnetization) of two variables : . We are interested in the behavior of minimizers as . They are expected to be -valued maps of vanishing distributional divergence , so that appropriate boundary conditions enforce line discontinuities. For finite , these line discontinuities are approximated by smooth transition layers, the so-called Néel...
Rochdi Jebari, Abderrahman Boukricha (2015)
Commentationes Mathematicae Universitatis Carolinae
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This paper concerns the following system of nonlinear third-order boundary value problem: with the following multi-point and integral boundary conditions: where , , and are continuous functions for all and . Using Guo-Krasnosel’skii fixed point theorem in cone, we discuss the existence of positive solutions of this problem. We also prove nonexistence of positive solutions and we give some examples to illustrate our results.
A. J. Irving (2015)
Acta Arithmetica
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Improving on a theorem of Heath-Brown, we show that if X is sufficiently large then a positive proportion of the values n³ + 2: n ∈ (X,2X] have a prime factor larger than .
Miloš Arsenović, Dragoljub Kečkić (2006)
Studia Mathematica
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We consider elementary operators , acting on a unital Banach algebra, where and 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 and , i.e. (), where all and ( and ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class...
Volodymyr Mykhaylyuk, Anatolij Plichko (2015)
Colloquium Mathematicae
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We comment on a problem of Mazur from “The Scottish Book" concerning second partial derivatives. We prove that if a function f(x,y) of real variables defined on a rectangle has continuous derivative with respect to y and for almost all y the function has finite variation, then almost everywhere on the rectangle the partial derivative exists. We construct a separately twice differentiable function whose partial derivative is discontinuous with respect to the second variable on a...
N. Parhi, S. Parhi (1986)
Annales Polonici Mathematici
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Jianwen Zhou, Yongkun Li (2011)
Annales Polonici Mathematici
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Some sufficient conditions on the existence and multiplicity of solutions for the damped vibration problems with impulsive effects ⎧ u”(t) + g(t)u’(t) + f(t,u(t)) = 0, a.e. t ∈ [0,T ⎨ u(0) = u(T) = 0 ⎩ , j = 1,...,p, are established, where , g ∈ L¹(0,T;ℝ), f: [0,T] × ℝ → ℝ is continuous, and , j = 1,...,p, are continuous. The solutions are sought by means of the Lax-Milgram theorem and some critical point theorems. Finally, two examples are presented to illustrate the effectiveness...
S. Sędziwy (1969)
Annales Polonici Mathematici
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Svetlana Roudenko (2004)
Studia Mathematica
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We determine the duals of the homogeneous matrix-weighted Besov spaces and which were previously defined in [5]. If W is a matrix weight, then the dual of can be identified with and, similarly, . Moreover, for certain W which may not be in the class, the duals of and are determined and expressed in terms of the Besov spaces and , which we define in terms of reducing operators associated with W. We also develop the basic theory of these reducing operator Besov spaces....
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 . For λ > 0, suppose that denotes any one of the following classes of functions: , , . The main purpose of this paper is to find conditions on λ and γ so that each f ∈ is in or , γ ∈ [0,1/2]. Here and 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...
S. Ponnusamy, A. Vasudevarao, M. Vuorinen (2009)
Colloquium Mathematicae
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For μ ∈ ℂ such that Re μ > 0 let denote the class of all non-vanishing analytic functions f in the unit disk with f(0) = 1 and in . For any fixed z₀ in the unit disk, a ∈ ℂ with |a| ≤ 1 and λ ∈ ̅, we shall determine the region of variability V(z₀,λ) for log f(z₀) when f ranges over the class . In the final section we graphically illustrate the region of variability for several sets of parameters.
A. El-Haffaf (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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This paper treats the question of the existence of solutions of a fourth order boundary value problem having the following form: , 0 < t < 1, x(0) = x’(0) = 0, x”(1) = 0, . Boundary value problems of very similar type are also considered. It is assumed that f is a function from the space C([0,1]×ℝ²,ℝ). The main tool used in the proof is the Leray-Schauder nonlinear alternative.
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 , where , , with 0 < ρ < 1 and R an orthogonal transformation of . Then ⎧1 < p ≤ 2 ⇒ ⎨, , ⎩ p = 2 ⇒ infr≥1 rd(1/α’-1/2) (∫J₀r|μ̂(y)|² dy)1/2 ≥ D₂ρd/α’where , α’ is defined by and the constants D₁ and D₂ depend only on d and p.
Jian-Lin Li (2006)
Studia Mathematica
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Let M ∈ Mₙ(ℤ) be expanding such that |det(M)| = p is a prime and pℤⁿ ⊈ M²(ℤⁿ). Let D ⊂ ℤⁿ be a finite set with |D| = |det(M)|. Suppose the attractor T(M,D) of the iterated function system has positive Lebesgue measure. We prove that (i) if D ⊈ M(ℤⁿ), then D is a complete set of coset representatives of ℤⁿ/M(ℤⁿ); (ii) if D ⊆ M(ℤⁿ), then there exists a positive integer γ such that , where D₀ is a complete set of coset representatives of ℤⁿ/M(ℤⁿ). This improves the corresponding results...
Feng-Juan Chen, Yong-Gao Chen (2014)
Colloquium Mathematicae
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Suppose that N is an odd perfect number and is a prime power with . Define the index . We prove that m cannot take the form , where u is a positive integer and 2u+1 is composite. We also prove that, if q is the Euler prime, then m cannot take any of the 30 forms q₁, q₁², q₁³, q₁⁴, q₁⁵, q₁⁶, q₁⁷, q₁⁸, q₁q₂, q₁²q₂, q₁³q₂, q₁⁴ q₂, q₁⁵q₂, q₁²q₂², q₁³q₂², q₁⁴q₂², q₁q₂q₃, q₁²q₂q₃, q₁³q₂q₃, q₁⁴q₂q₃, q₁²q₂²q₃, q₁²q₂²q₃², q₁q₂q₃q₄, q₁²q₂q₃q₄, q₁³q₂q₃q₄, q₁²q₂²q₃q₄, q₁q₂q₃q₄q₅, q₁²q₂q₃q₄q₅,...
Jean Mawhin, Katarzyna Szymańska-Dębowska (2016)
Mathematica Bohemica
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A couple () of lower and upper slopes for the resonant second order boundary value problem with increasing on such that , is a couple of functions such that for all , in the stripe and . It is proved that the existence of such a couple implies the existence and localization of a solution to the boundary value problem. Multiplicity results are also obtained.