Search results for "Phase plane analysis"
showing 4 items of 4 documents
Elektro-Okulographie bei Hirnstammerkrankungen
2011
Zusammenfassung Augenbewegungsstorungen sind haufige und typische Symptomen von Hirnstammerkrankungen. Hier liegt die Bedeutung der Elektrookulographie in erster Linie in der Aufdeckung subklinischer Veranderungen (Abb. 1) und weniger in der Bestatigung klinisch evidenter Storungen. Hierzu eignet sich vor allem die Aufzeichnung von Willkursakkaden, die im Allgemeinen bezuglich Geschwindigkeit und Zielgenauigkeit analysiert werden. Hiermit konnen bei Patienten mit multipler Sklerose oder Bewegungsstorungen (M. Parkinson, progressive supranukleare Parese, Chorea Huntington) eine Reihe recht typischer Befunde erhoben werden, die bei der Diagnose hilfreich sein konnen. Dabei legen neuere Studie…
Multiplicity of ground states for the scalar curvature equation
2019
We study existence and multiplicity of radial ground states for the scalar curvature equation $$\begin{aligned} \Delta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n, \quad n>2, \end{aligned}$$when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ is bounded above and below by two positive constants, i.e. $$0 0$$, it is decreasing in (0, 1) and increasing in $$(1,+\infty )$$. Chen and Lin (Commun Partial Differ Equ 24:785–799, 1999) had shown the existence of a large number of bubble tower solutions if K is a sufficiently small perturbation of a positive constant. Our main purpose is to improve such a result by considering a non-perturbative situation: we ar…
Multiplicity of Radial Ground States for the Scalar Curvature Equation Without Reciprocal Symmetry
2022
AbstractWe study existence and multiplicity of positive ground states for the scalar curvature equation $$\begin{aligned} \varDelta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n\,, \quad n>2, \end{aligned}$$ Δ u + K ( | x | ) u n + 2 n - 2 = 0 , x ∈ R n , n > 2 , when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ K : R + → R + is bounded above and below by two positive constants, i.e. $$0<\underline{K} \le K(r) \le \overline{K}$$ 0 < K ̲ ≤ K ( r ) ≤ K ¯ for every $$r > 0$$ r > 0 , it is decreasing in $$(0,{{{\mathcal {R}}}})$$ ( 0 , R ) and increasing in $$({{{\mathcal {R}}}},+\infty )$$ ( R , + ∞ ) for a certain $${{{\mathcal {R}}}}&g…
Phase Plane Analysis of Web Drying
2004
The mathematical model which describes the web drying in the papermaking machine has been carried out in the collaboration between our institute and joint-stock company “Paper Mill ‘Ligatne’” engineers. The general principles of this develpopment were underlined in the report [zz00]. Under some simplifying assumptions this model can be reduced to the nonlinear moisture — temperature phase plane equation. This equation promotes to obtain significant physical parameters used in the mathematical model, clarifies the causes which allow to optimize the papermaking machine drying cylinders temperature regime. The phase plane equation also explains the parabolic temperature distribution in a serie…