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Rectifiable and Unrectifiable Oscillations for a Generalization of the Riemann–Weber Version of Euler Differential Equation
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Mervan Pašić
Published/Copyright:
March 11, 2010
Abstract
The following generalization

(for α = 2 we suppose that β = 2 and λ > 1/4), of the Riemann–Weber version of Euler differential equation is introduced and it is considered together with a suitable boundary layer condition depending on α near 𝑥 = 0. It is shown that this problem is rectifiable (resp., unrectifiable) oscillatory on (0, 𝑏) provided α ∈ [2, 4) (resp., α ≥ 4). It is a kind of geometrical oscillations on (0, 𝑏) for which the finite (resp., infinite) length of the graphs of all its solutions is proposed.
Key words and phrases:: Linear; singular; Riemann–Weber version of Euler equation; oscillations; Sturm's comparison principle; graph; rectifiability; unrectifiability
Received: 2007-01-22
Revised: 2007-03-29
Published Online: 2010-03-11
Published in Print: 2008-December
© Heldermann Verlag
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Keywords for this article
Linear;
singular;
Riemann–Weber version of Euler equation;
oscillations;
Sturm's comparison principle;
graph;
rectifiability;
unrectifiability
Articles in the same Issue
- On Iterative Combination of Modified Bernstein-Type Polynomials
- On Dynamical Three-Dimensional Fluid-Solid Interaction Problem
- Existence and Uniqueness of Weak Solution for a Class of Elliptic Reaction-Diffusion Systems
- Existence of Solutions in Weighted Sobolev Spaces for Some Degenerate Quasilinear Elliptic Equations
- Periodic Solutions for Nonlinear Differential Equation with Functional Delay
- Restriction Theorems for Anisotropically Homogeneous Hypersurfaces of
- Dual Variational Method for a Fourth Order Dirichlet Problem
- On Some Combinatorial Problems Concerning Geometrical Realizations of Finite and Infinite Families of Sets
- Beurling–Borg Type Theorem for Two-Dimensional Linear Differential Systems
- The Maximal Operator in Weighted Variable Exponent Spaces on Metric Spaces
- Sequential Detection of Drift Change for Brownian Motion with Unknown Sign
- Uniqueness for Meromorphic Functions Concerning Differential Polynomials
- Integral Representations and Continuous Projectors in Some Spaces of Analytic and Pluriharmonic Functions
- On One Problem with the Condition at Infinity for Second Order Singular Ordinary Differential Equations
- Rectifiable and Unrectifiable Oscillations for a Generalization of the Riemann–Weber Version of Euler Differential Equation
- Compact Composition Operators on Generalized Hardy Spaces
- CLT for Operator Abel Sums of Random Elements
- On the Dirichlet Problem for a Second Order Elliptic System with Degeneration on the Whole Boundary of a Multidimensional Domain
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