scholarly journals Asymptotics of a fundamental solution system for a quasidifferential equation with measures on the semiaxis

2014 ◽  
Vol 6 (1) ◽  
pp. 113-122
Author(s):  
O.V. Makhnei
Keyword(s):  
Fundamental Solution ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Asymptotic Formulas ◽  
Solution System ◽  
Asymptotics Of Eigenvalues ◽  
Eigenvalues And Eigenfunctions ◽  
Quasidifferential Equation

With the help of a conception of quasiderivatives asymptotic formulas for a fundamental solution system of a quasidifferential equation with measures on the semiaxis $[0,\infty)$ are constructed. The obtained asymptotic formulas allow to investigate asymptotics of eigenvalues and eigenfunctions of the corresponding boundary value problem.

scholarly journals ASYMPTOTIC DISTRIBUTION OF EIGENVALUES AND EIGENFUNCTIONS OF A NONLOCAL BOUNDARY VALUE PROBLEM

2021 ◽  
Vol 26 (2) ◽  
pp. 253-266
Author(s):  
Erdoğan Şen ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Asymptotic Distribution ◽  
Nonlocal Boundary Condition ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Asymptotic Formulas ◽  
Nonlocal Boundary Value Problem ◽  
Eigenvalues And Eigenfunctions ◽  
Distribution Of Eigenvalues

In this work, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the second order boundary-value problem with a Bitsadze–Samarskii type nonlocal boundary condition.

scholarly journals Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Erdoğan Şen ◽  
Jong Jin Seo ◽  
Serkan Araci
Keyword(s):  
Boundary Value Problem ◽  
Liouville Operator ◽  
Liouville Problem ◽  
Asymptotic Formulas ◽  
Retarded Argument ◽  
Eigenvalues And Eigenfunctions ◽  
Transmission Coefficients ◽  
Discontinuous Boundary ◽  
Sturm Liouville ◽  
Special Case

In the present paper, a discontinuous boundary-value problem with retarded argument at the two points of discontinuities is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. This is the first work containing two discontinuities points in the theory of differential equations with retarded argument. In that special case the transmission coefficients and retarded argument in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.

Spectral Problem for a Polynomial Pencil of the Sturm-Liouville Equations

2020 ◽  
pp. 163-181
Author(s):  
Anar Adiloğlu-Nabiev
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Spectral Problem ◽  
Boundary Value ◽  
Asymptotic Formulas ◽  
Complex Numbers ◽  
Arbitrary Complex ◽  
Sturm Liouville ◽  
Complex Valued

A boundary value problem for the second order differential equation -y′′+∑_{m=0}N−1λ^{m}q_{m}(x)y=λ2Ny with two boundary conditions a_{i1}y(0)+a_{i2}y′(0)+a_{i3}y(π)+a_{i4}y′(π)=0, i=1,2 is considered. Here n>1, λ is a complex parameter, q0(x),q1(x),...,q_{n-1}(x) are summable complex-valued functions, a_{ik} (i=1,2; k=1,2,3,4) are arbitrary complex numbers. It is proved that the system of eigenfunctions and associated eigenfunctions is complete in the space and using elementary asymptotical metods asymptotic formulas for the eigenvalues are obtained.

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