All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 247

Showing per page

Differential equations in metric spaces

Jacek Tabor (2002)

Mathematica Bohemica

We give a meaning to derivative of a function u ℝ → X , where X is a complete metric space. This enables us to investigate differential equations in a metric space. One can prove in particular Gronwall’s Lemma, Peano and Picard Existence Theorems, Lyapunov Theorem or Nagumo Theorem in metric spaces. The main idea is to define the tangent space 𝒯 x X of x ∈ X . Let u , v [ 0 , 1 ) → X , u ( 0 ) = v ( 0 ) be continuous at zero. Then by the definition u and v are in the same equivalence class if they are tangent at zero, that is if lim h → 0 + d ( u ( h ) , v ( h ) ) h = 0 . By 𝒯 x X we denote...

Differential equations on the plane with given solutions.

R. Ramírez, N. Sadovskaia (1996)

Collectanea Mathematica

The aim of this paper is to construct the analytic vector fields with given as trajectories or solutions. In particular we construct the polynomial vector field from given conics (ellipses, hyperbola, parabola, straight lines) and determine the differential equations from a finite number of solutions.

Examples of bifurcation of periodic solutions to variational inequalities in ℝ κ

Milan Kučera (2000)

Czechoslovak Mathematical Journal

A bifurcation problem for variational inequalities U ( t ) ∈ K , ( U ˙ ( t ) - B λ U ( t ) - G ( λ , U ( t ) ) , Z - U ( t ) ) ≥ 0 for all Z ∈ K , a.a. t ≥ 0 is studied, where K is a closed convex cone in ℝ κ , κ ≥ 3 , B λ is a κ × 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.

Currently displaying 61 – 80 of 247