On the behaviour of solutions of the differential equations
N. Parhi, S. Parhi (1986)
Annales Polonici Mathematici
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N. Parhi, S. Parhi (1986)
Annales Polonici Mathematici
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Jan Andres, Jan Vorácek (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Si dimostra un teorema di esistenza di soluzioni periodiche dell'equazione differenziale ordinaria del terzo ordine con le funzioni , , periodiche in di periodo .
Jan Andres, Jan Vorácek (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si dimostra un teorema di esistenza di soluzioni periodiche dell'equazione differenziale ordinaria del terzo ordine con le funzioni , , periodiche in di periodo .
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 .
S. Sędziwy (1969)
Annales Polonici Mathematici
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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.
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.
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.
M. Kisielewicz (1977)
Colloquium Mathematicae
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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.
Jiří Šremr (2025)
Czechoslovak Mathematical Journal
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We study the existence and uniqueness of a positive solution to the problem with a super-linear nonlinearity and a nontrivial forcing term . To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case.
Houyu Zhao, Jianguo Si (2009)
Annales Polonici Mathematici
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We study existence of analytic solutions of a second-order iterative functional differential equation in the complex field ℂ. By constructing an invertible analytic solution y(z) of an auxiliary equation of the form invertible analytic solutions of the form for the original equation are obtained. Besides the hyperbolic case 0 < |α| < 1, we focus on α on the unit circle S¹, i.e., |α|=1. We discuss not only those α at resonance, i.e. at a root of unity, but also near resonance...
Mariusz Ska/lba (2005)
Colloquium Mathematicae
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A classical theorem of M. Fried [2] asserts that if non-zero integers have the property that for each prime number p there exists a quadratic residue mod p then a certain product of an odd number of them is a square. We provide generalizations for power residues of degree n in two cases: 1) n is a prime, 2) n is a power of an odd prime. The proofs involve some combinatorial properties of finite Abelian groups and arithmetic results of [3].
Florian Luca, Pantelimon Stănică (2003)
Colloquium Mathematicae
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We show that if p ≠ 5 is a prime, then the numbers cover all the nonzero residue classes modulo p.
Artūras Dubickas (2006)
Acta Mathematica Universitatis Ostraviensis
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We are interested whether there is a nonnegative integer and an infinite sequence of digits in base such that the numbers where are all prime or at least do not have prime divisors in a finite set of prime numbers If any such sequence contains infinitely many elements divisible by at least one prime number then we call the set unavoidable with respect to . It was proved earlier that unavoidable sets in base exist if and that no unavoidable set exists in base Now,...
Michał Kisielewicz (1979)
Annales Polonici Mathematici
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Quang A Dang, Quang Long Dang (2021)
Applications of Mathematics
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We consider the boundary value problem where , are continuous functions. The case when was studied in 2018 by Guendouz et al. Using the fixed-point theory on cones they established the existence of positive solutions. Here, by the method developed by ourselves very recently, we establish the existence, uniqueness and positivity of the solution under easily verified conditions and propose an iterative method for finding the solution. Some examples demonstrate the validity of the...
Eva Tesaříková (1987)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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