Periodic solutions of
W. R. Utz (1971)
Annales Polonici Mathematici
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W. R. Utz (1971)
Annales Polonici Mathematici
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J. W. Heidel (1971)
Annales Polonici Mathematici
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J. W. Heidel (1973)
Annales Polonici Mathematici
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Yongxiang Li, He Yang (2011)
Annales Polonici Mathematici
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The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation , where is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity to guarantee the existence and uniqueness are presented. These conditions extend and improve the ones presented by Cong [Appl. Math. Lett. 17 (2004), 727-732].
Viktor Harangi (2011)
Fundamenta Mathematicae
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Let be arbitrary nonzero real numbers. An -decomposition of a function f:ℝ → ℝ is a sum where is an -periodic function. Such a decomposition is not unique because there are several solutions of the equation with -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the -decomposition is essentially unique. We characterize those periods for which essential...
Jian Hua Yin, Jia-Yun Li, Jin-Zhi Du, Hai-Yan Li (2019)
Czechoslovak Mathematical Journal
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Let be the complete bipartite graph with partite sets and . A split bipartite-graph on vertices, denoted by , is the graph obtained from by adding new vertices , such that each of is adjacent to each of and each of is adjacent to each of . Let and be nonincreasing lists of nonnegative integers, having lengths and , respectively. The pair is potentially -bigraphic if there is a simple bipartite graph containing (with vertices in the part of size ...
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.
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.
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...
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...
Zhi-Hong Sun (2021)
Czechoslovak Mathematical Journal
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Let be the Ramsey number of the two graphs and . For let be the double star given by , and . We determine under certain conditions. For let , and , where , , and . We also obtain explicit formulas for , , , and , where , is the path on vertices and is the unique tree with vertices and maximal degree .
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....
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....
Imene Soulahia, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)
Commentationes Mathematicae Universitatis Carolinae
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The fixed point theorem of Krasnoselskii and the concept of large contractions are employed to show the existence of a periodic solution of a nonlinear integro-differential equation with variable delay We transform this equation and then invert it to obtain a sum of two mappings one of which is completely continuous and the other is a large contraction. We choose suitable conditions for , , , and to show that this sum of mappings fits into the framework of a modification of...
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.
Mark L. Lewis, Yanjun Liu, Hung P. Tong-Viet (2018)
Czechoslovak Mathematical Journal
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Let be a finite group and write for the degree set of the complex irreducible characters of . The group is said to satisfy the two-prime hypothesis if for any distinct degrees , the total number of (not necessarily different) primes of the greatest common divisor is at most . We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL for .
Ryôhei Kakizawa (2018)
Czechoslovak Mathematical Journal
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We discuss the validity of the Helmholtz decomposition of the Muckenhoupt -weighted -space for any domain in , , , and Muckenhoupt -weight . Set and . Then the Helmholtz decomposition of and and the variational estimate of and are equivalent. Furthermore, we can replace and by and , respectively. The proof is based on the reflexivity and orthogonality of and and the Hahn-Banach theorem. As a corollary of our main result, we obtain the extrapolation...