Displaying similar documents to “Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis”

On peaks in carrying simplices

Janusz Mierczyński (1999)

Colloquium Mathematicae

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A necessary and sufficient condition is given for the carrying simplex of a dissipative totally competitive system of three ordinary differential equations to have a peak singularity at an axial equilibrium. For systems of Lotka-Volterra type that result translates into a simple condition on the coefficients.

On the basis property of the root functions of differential operators with matrix coefficients

Oktay Veliev (2011)

Open Mathematics

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We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these asymptotic formulas, we find necessary and sufficient conditions on the coefficients for which the system of eigenfunctions and associated functions of the operator under consideration forms a Riesz basis.

Time asymptotic description of an abstract Cauchy problem solution and application to transport equation

Boulbeba Abdelmoumen, Omar Jedidi, Aref Jeribi (2014)

Applications of Mathematics

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In this paper, we study the time asymptotic behavior of the solution to an abstract Cauchy problem on Banach spaces without restriction on the initial data. The abstract results are then applied to the study of the time asymptotic behavior of solutions of an one-dimensional transport equation with boundary conditions in L 1 -space arising in growing cell populations and originally introduced by M. Rotenberg, J. Theoret. Biol. 103 (1983), 181–199.