Weak Wecken's theorem for periodic points in dimension 3

Jerzy Jezierski

Displaying similar documents to “Weak Wecken's theorem for periodic points in dimension 3”

Periodic solutions to a non-linear differential equation of the order $2n+1$

Monika Kubicova (1989)

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

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A criterion for the existance of periodic solutions of an ordinary differential equation of order k proved by J. Andres and J. Vorâcek for k = 3 is extended to an arbitrary odd k.

Periodic solutions to a non-linear differential equation of the order $2n+1$

Monika Kubicova (1989)

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

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A criterion for the existance of periodic solutions of an ordinary differential equation of order k proved by J. Andres and J. Vorâcek for k = 3 is extended to an arbitrary odd k.

Existence and uniqueness of periodic solutions for odd-order ordinary differential equations

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 $u^{(2 n + 1)} = f (t, u, u^{'}, . . ., u^{(2 n)})$ , where $f : ℝ \times ℝ^{2 n + 1} \to ℝ$ is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity $f (t, x ₀, x ₁, . . ., x_{2 n})$ 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].

Periodic solutions of evolution problem associated with moving convex sets

Charles Castaing, Manuel D.P. Monteiro Marques (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form $- D u \in N_{C (t)} (u (t)) + f (t, u (t))$ where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, $N_{C (t)} (u (t))$ is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions...

Minimal number of periodic points for smooth self-maps of S³

Grzegorz Graff, Jerzy Jezierski (2009)

Fundamenta Mathematicae

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Let f be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3 and r a fixed natural number. A topological invariant $D_{r}^{m} [f]$ , introduced by the authors [Forum Math. 21 (2009)], is equal to the minimal number of r-periodic points for all smooth maps homotopic to f. In this paper we calculate $D ³_{r} [f]$ for all self-maps of S³.

Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters

Shu-Gui Kang, Bao Shi, Sui Sun Cheng (2009)

Annales Polonici Mathematici

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Existence of periodic solutions of functional differential equations with parameters such as Nicholson’s blowflies model call for the investigation of integral equations with parameters defined over spaces with periodic structures. In this paper, we study one such equation $ϕ (x) = λ \int_{[x, x + ω] \cap Ω} K (x, y) h (y) f (y, ϕ (y - τ (y))) d y$ , x ∈ Ω, by means of the proper value theory of operators in Banach spaces with cones. Existence, uniqueness and continuous dependence of proper solutions are established.

Addenda to “Periodic solutions of $x " + f (x) x^{' 2 n} + g (x) = 0$ with arbitrarily large period”

J. W. Heidel (1973)

Annales Polonici Mathematici

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Periodic solutions of $x " + f (x) x^{' 2 n} + g (x) = 0$ with arbitrarily large period

J. W. Heidel (1971)

Annales Polonici Mathematici

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Multiple positive solutions of a nonlinear fourth order periodic boundary value problem

Lingbin Kong, Daqing Jiang (1998)

Annales Polonici Mathematici

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The fourth order periodic boundary value problem $u^{(4)} - m ⁴ u + F (t, u) = 0$ , 0 < t < 2π, with $u^{(i)} (0) = u^{(i)} (2 π)$ , i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of $\pm 10^{- 7}$ .

Periodic solutions of a weakly nonlinear wave equation in $E_{3}$ in a spherically symmetrical case

Otto Vejvoda (1969)

Aplikace matematiky

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In the paper the conditions for the existence of a $2 π$ -periodic solution in $t$ of the system $u_{t t} - u_{r r} - (2 / r) u_{r} = ϵ f (t, r, u, u_{t}, u_{r})$ , $|u (t, 0)| < + \infty, u (t, π) = 0$ are investigated provided that $f$ is sufficiently smooth and $2 π$ -periodic in $t$ .

Periodic Solutions of Periodic Retarded Functional Differential Equations

Marcin Pawłowski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (RFDE) $x^{'} (t) = f (t, x_{t})$ , where f is T-periodic in t. We construct a pair of subsets of ℝ × ℝⁿ called a T-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a T-periodic solution.

A class of $I_{0}$ -sets

David Grow (1987)

Colloquium Mathematicae

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Periodic solutions of $x " + f (x) x^{' m} + g (x) = 0$

W. R. Utz (1971)

Annales Polonici Mathematici

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Three periodic solutions for a class of higher-dimensional functional differential equations with impulses

Yongkun Li, Changzhao Li, Juan Zhang (2010)

Annales Polonici Mathematici

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By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ⎧y’(t) = A(t)y(t) + g(t,yt), $t \neq t_{j}$ , j ∈ ℤ, ⎨ ⎩ $y (t ⁺_{j}) = y (t ¯_{j}) + I_{j} (y (t_{j}))$ , where $A (t) = {(a_{i j} (t))}_{n \times n}$ is a nonsingular matrix with continuous real-valued entries.

Anti-periodic solutions to a parabolic hemivariational inequality

Jong Yeoul Park, Hyun Min Kim, Sun Hye Park (2004)

Kybernetika

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In this paper we deal with the anti-periodic boundary value problems with nonlinearity of the form $b (u)$ , where $b \in L_{loc}^{\infty} (R) .$ Extending $b$ to be multivalued we obtain the existence of solutions to hemivariational inequality and variational-hemivariational inequality.

Characterising weakly almost periodic functionals on the measure algebra

Matthew Daws (2011)

Studia Mathematica

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Let G be a locally compact group, and consider the weakly almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C*-subalgebra of the commutative C*-algebra M(G)*, and so has character space, say $K_{W A P}$ . In this paper, we investigate properties of $K_{W A P}$ . We present a short proof that $K_{W A P}$ can naturally be turned into a semigroup whose product is separately continuous; at the Banach algebra level, this product is simply the natural one induced by the Arens...

Dissipative Euler flows and Onsager's conjecture

Camillo De Lellis, László Székelyhidi (2014)

Journal of the European Mathematical Society

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Building upon the techniques introduced in [15], for any $θ < \frac{1}{10}$ we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are Hölder-continuous with exponent $θ$ . A famous conjecture of Onsager states the existence of such dissipative solutions with any Hölder exponent $θ < \frac{1}{3}$ . Our theorem is the first result in this direction.

On the solution set of the nonconvex sweeping process

Andrea Gavioli (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We prove that the solutions of a sweeping process make up an $R_{δ}$ -set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.

Existence of nonnegative periodic solutions in neutral integro-differential equations with functional delay

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 $x^{'} (t) = - \int_{t - τ (t)}^{t} a (t, s) g (x (s)) d s + \frac{d}{d t} Q (t, x (t - τ (t))) + G (t, x (t), x (t - τ (t))) .$ 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 $τ$ , $g$ , $a$ , $Q$ and $G$ to show that this sum of mappings fits into the framework of a modification of...