Global attractivity of the equilibrium of a nonlinear difference equation

summary:The authors consider the nonlinear difference equation $$x_{n+1}=\alpha x_n + x_{n-k}f(x_{n-k}), \quad n=0, 1,\dots .1 \text{where} \alpha \in (0, 1),\hspace{5.0pt}k \in \lbrace 0, 1, \dots \rbrace \hspace{5.0pt}\text{and}\hspace{5.0pt}f\in C^1[[0, \infty ),[0, \infty )] \qquad \mathrm{(0)}$$ with $f^{\prime }(x)<0$. They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given

Existence of positive solutions to multi-point third order problems with sign changing nonlinearities

In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign changing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results

Positive solutions of a fourth-order differential equation with integral boundary conditions

summary:We study the existence of positive solutions to the fourth-order two-point boundary value problem $$\begin {cases} u^{\prime \prime \prime \prime }(t) + f(t,u(t))=0, & 0 < t < 1,\\ u^{\prime }(0) = u^\prime (1) = u^{\prime \prime }(0) =0, & u(0) = \alpha [u], \end {cases}$$ where $\alpha [u]=\int ^{1}_{0}u(t){\rm d}A(t)$ is a Riemann-Stieltjes integral with $A \geq 0$ being a nondecreasing function of bounded variation and $f \in \mathcal {C}([0,1] \times \mathbb {R}_{+}, \mathbb {R}_{+})$. 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

Wave Dynamical Chaos in a Superconducting Three-Dimensional Sinai Billiard

Based on very accurate measurements performed on a superconducting microwave resonator shaped like a desymmetrized three-dimensional (3D) Sinai billiard, we investigate for the first time spectral properties of the vectorial Helmholtz, i.e. non-quantum wave equation for a classically totally chaotic and theoretically precisely studied system. We are thereby able to generalize some aspects of quantum chaos and present some results which are consequences of the polarization features of the electromagnetic waves.Comment: 4 pages RevTex; 4 postscript figures; to be published in Phys. Rev. Lett.; Info: [email protected]

Anderson Localization in a String of Microwave Cavities

The field distributions and eigenfrequencies of a microwave resonator which is composed of 20 identical cells have been measured. With external screws the periodicity of the cavity can be perturbed arbitrarily. If the perturbation is increased a transition from extended to localized field distributions is observed. For very large perturbations the field distributions show signatures of Anderson localization, while for smaller perturbations the field distribution is extended or weakly localized. The localization length of a strongly localized field distribution can be varied by adjusting the penetration depth of the screws. Shifts in the frequency spectrum of the resonator provide further evidence for Anderson localization.Comment: 7 pages RevTex, to be published in Phys. Rev.

Statebuilding and narrative

In recent years, narrative approaches have become increasingly popular in the study of peaceand statebuilding. Yet, the conceptual and empirical idiosyncrasies of stories and storytelling are rarely acknowledged. This chapter provides an overview of the uses of narrative in the field to date. It highlights its value for understanding power imbalances, the complexity of human experiences and knowledge creation, and ethical challenges connected to fieldwork. Engaging in greater depth with conceptual and analytical perspectives on narrative, not least by drawing on insights from related social science disciplines, will help to uncover the unique contribution these perspectives can make to researching and practicing peace- and statebuilding.info:eu-repo/semantics/submittedVersio

Boundedness and convergence to zero of solutions of a forced second-order nonlinear differential equation

AbstractSufficient conditions for continuability, boundedness, and convergence to zero of solutions of (a(t)x′)′ + h(t, x, x′) + q(t) f(x) g(x′) = e(t, x, x′) are given

Mode Fluctuation Distribution for Spectra of Superconducting Microwave Billiards

High resolution eigenvalue spectra of several two- and three-dimensional superconducting microwave cavities have been measured in the frequency range below 20 GHz and analyzed using a statistical measure which is given by the distribution of the normalized mode fluctuations. For chaotic systems the limit distribution is conjectured to show a universal Gaussian, whereas integrable systems should exhibit a non-Gaussian limit distribution. For the investigated Bunimovich stadium and the 3D-Sinai billiard we find that the distribution is in good agreement with this prediction. We study members of the family of limacon billiards, having mixed dynamics. It turns out that in this case the number of approximately 1000 eigenvalues for each billiard does not allow to observe significant deviations from a Gaussian, whereas an also measured circular billiard with regular dynamics shows the expected difference from a Gaussian.Comment: 7 pages, RevTex, 5 postscript figure, to be published in Phys. Rev. E. In case of any problems contact A. Baecker ([email protected]) or H. Rehfeld ([email protected]

A class of nth-order BVPs with nonlocal conditions

AbstractThe aim of this paper is to present some existence results for a nonlinear nth-order boundary value problem with nonlocal conditions. Various fixed point theorems are used in the proofs. Examples are included to illustrate the results