A differential equation related to the $l^{p}$-norms

• Autorzy: Jacek Bojarski , Tomasz Małolepszy , Janusz Matkowski
• Języki publikacji: EN

Abstrakty

EN

Let p ∈ (1,∞). The question of existence of a curve in ℝ₊² starting at (0,0) and such that at every point (x,y) of this curve, the $l^{p}$-distance of the points (x,y) and (0,0) is equal to the Euclidean length of the arc of this curve between these points is considered. This problem reduces to a nonlinear differential equation. The existence and uniqueness of solutions is proved and nonelementary explicit solutions are given.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B45: Banach sequence spaces
• 34A34: Nonlinear equations and systems, general

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2011
• Tom: 101
• Numer: 3
• Strony: 251-265

Daty

wydano

2011

Twórcy

autor

Jacek Bojarski

• Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

autor

Tomasz Małolepszy

• Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

autor

Janusz Matkowski

• Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
• Institute of Mathematics, Silesian University, Bankowa 14, 40-007, Katowice, Poland

Identyfikatory

DOI

10.4064/ap101-3-5