Bifurcation of periodic solutions to differential inequalities in $\mathbb {R}^3$

Miroslav Bosák; Milan Kučera

Displaying similar documents to “Bifurcation of periodic solutions to differential inequalities in $ℝ^{3}$ ”

Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas

Hans-Otto Walther

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CONTENTSIntroduction...........................................................................................................................................5 I.........................................................................................................................................................151. Preliminaries...................................................................................................................................152. Solutions of a family...

Examples of bifurcation of periodic solutions to variational inequalities in $ℝ^{κ}$

Milan Kučera (2000)

Czechoslovak Mathematical Journal

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A bifurcation problem for variational inequalities $U (t) \in K, (\dot{U} (t) - B_{λ} U (t) - G (λ, U (t)), Z - U (t)) \geq 0 for all Z \in K, a.a. t \geq 0$ is studied, where $K$ is a closed convex cone in $ℝ^{κ}$ , $κ \geq 3$ , $B_{λ}$ is a $κ \times κ$ matrix, $G$ is a small perturbation, $λ$ a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.

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].

Exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems

Shao-Yuan Huang, Ping-Han Hsieh (2023)

Czechoslovak Mathematical Journal

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We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems $\{\begin{matrix} - {[φ (u^{'})]}^{'} = λ u^{p} (1 - \frac{u}{N}) & in (- L, L), \\ u (- L) = u (L) = 0, \end{matrix}$ where $p > 1$ , $N > 0$ , $λ > 0$ is a bifurcation parameter, $L > 0$ is an evolution parameter, and $φ (u)$ is either $φ (u) = u$ or $φ (u) = u / \sqrt{1 - u^{2}}$ . We prove that the corresponding bifurcation curve is $\subset$ -shape. Thus, the exact multiplicity of positive solutions can be obtained.

Generalized $c$ -almost periodic type functions in $ℝ^{n}$

M. Kostić (2021)

Archivum Mathematicum

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In this paper, we analyze multi-dimensional quasi-asymptotically $c$ -almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl $c$ -almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically $c$ -almost periodic functions and reconsider the notion of semi- $c$ -periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide...

Bifurcation theorems for nonlinear problems with lack of compactness

Francesca Faraci, Roberto Livrea (2003)

Annales Polonici Mathematici

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We deal with a bifurcation result for the Dirichlet problem ⎧ $- Δ_{p} u = μ / {| x |}^{p} {| u |}^{p - 2} u + λ f (x, u)$ a.e. in Ω, ⎨ ⎩ $u_{| \partial Ω} = 0$ . Starting from a weak lower semicontinuity result by E. Montefusco, which allows us to apply a general variational principle by B. Ricceri, we prove that, for μ close to zero, there exists a positive number $λ *_{μ}$ such that for every $λ \in] 0, λ *_{μ} [$ the above problem admits a nonzero weak solution $u_{λ}$ in $W ₀^{1, p} (Ω)$ satisfying $l i m_{λ \to 0 ⁺} | | u_{λ} | | = 0$ .

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.

Stable periodic solutions in scalar periodic differential delay equations

Anatoli Ivanov, Sergiy Shelyag (2023)

Archivum Mathematicum

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A class of nonlinear simple form differential delay equations with a $T$ -periodic coefficient and a constant delay $τ > 0$ is considered. It is shown that for an arbitrary value of the period $T > 4 τ - d_{0}$ , for some $d_{0} > 0$ , there is an equation in the class such that it possesses an asymptotically stable $T$ -period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The...

A class of $I_{0}$ -sets

David Grow (1987)

Colloquium Mathematicae

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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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Displaying similar documents to “Bifurcation of periodic solutions to differential inequalities in ℝ 3 ”

Displaying similar documents to “Bifurcation of periodic solutions to differential inequalities in $ℝ^{3}$ ”