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.
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 and where , , , , , and are real valued functions which depend at most on the arguments displayed explicitly and 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....
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.
Seshadev Padhi, John R. Graef (2023)
Mathematica Bohemica
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We study the existence of positive solutions to the fourth-order two-point boundary value problem where is a Riemann-Stieltjes integral with being a nondecreasing function of bounded variation and . The sufficient conditions obtained are new and easy to apply. Their approach is based on Krasnoselskii’s fixed point theorem and the Avery-Peterson fixed point theorem.
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.
Konan Charles Etienne Goli, Assohoun Adjé (2017)
Communications in Mathematics
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We study the existence of solutions of the system submitted to nonlinear coupled boundary conditions on where , with , are two increasing homeomorphisms such that , and , are two -Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.
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...
Shichun Yang, Florian Luca, Alain Togbé (2019)
Mathematica Bohemica
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Let be the sequence of all primes in ascending order. Using explicit estimates from the prime number theory, we show that if , then which improves a previous result of the second author.
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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