Irregular boundary value problems revisited

DOI10.1007/s00025-012-0281-7zbMath1266.34001OpenAlexW1966608982MaRDI QIDQ1759042

Gerhard Freiling

Publication date: 19 November 2012

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-012-0281-7

zbMATH Keywords

Birkhoff-regularityirregular boundary value problemsStone-regular boundary value problems

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Green's functions for ordinary differential equations (34B27) Boundary eigenvalue problems for ordinary differential equations (34B09) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

Related Items (8)

Irregular boundary value problem for the Sturm-Liouville operator ⋮ On an inverse transmission problem from complex eigenvalues ⋮ On a local solvability and stability of the inverse transmission eigenvalue problem ⋮ Nonlocal problem with multipoint perturbations of the Birkhoff strongly regular boundary conditions for an even-order differential operator ⋮ The nonlocal multipoint problem with Dirichlet-type conditions for an ordinary differential equation of even order with involution ⋮ On a regularization approach to the inverse transmission eigenvalue problem ⋮ Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks ⋮ Hidden symmetries in non-self-adjoint graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On uniform and \(L^ p\)-convergence of eigenfunction expansions for indefinite eigenvalue problems
• A Krein space approach to symmetric ordinary differential operators with an indefinite weigth function
• Completeness of eigenfunctions of one class of pencils of differential operators with constant coefficients
• Zur Vollständigkeit des Systems der Eigenfunktionen irregulärer Eigenwertprobleme mit \(\lambda\)-abhängigen Randbedingungen
• Multiple expansions in series of eigen- and associated functions of boundary eigenvalue problems nonlinearly dependent on the spectral parameter. II
• Oscillation properties for the equation of vibrating beam with irregular boundary conditions
• Resolvent growth and Birkhoff-regularity
• Multiple expansions in series of eigen- and associated functions of boundary eigenvalue problems nonlinearly dependent on the spectral parameter. I
• Irregular boundary value problems with discontinuous coefficients and the eigenvalue parameter
• On equiconvergence of spectral expansions of integral operators
• Spectral analysis of the Redge problem
• On the basis property of root elements of ordinary differential operators in the space \(L^2, n(a,b)\)
• Completeness of root functions of the simplest strongly irregular differential operators with two-point two-term boundary conditions
• Necessary conditions for the \(L_ 2\)-convergence of series in eigenfunctions of irregular eigenvalue problems
• Boundary problems for ordinary differential equations with parameter in the boundary conditions
• Completeness of the eigenfunctions of irregular differential operators in a space of vector-valued functions
• Irregular eigenvalue-problems on the half-axis
• Necessary conditions for the uniform convergence and Abel-summability of eigenfunction expansions with irregular ordinary differential bundles
• A generalization of Lebesgue's convergence criterion for Fourier series
• Reguläre Eigenwertprobleme mit Mehrpunkt-Integral-Randbedingungen
• Summability of eigenfunction expansions of differential operators and convolution operators
• On the distribution of the eigenvalues of a class of indefinite eigenvalue problems
• Expansion theorems for a class of regular indefinite eigenvalue problems
• Necessary conditions for the convergence and summability of eigenfunction expansions in the complex domain
• The distribution of the eigenvalues for second order eigenvalue problems in the presence of an arbitrary number of turning points
• Zur Vollständigkeit des Biorthogonalsystems von Eigenfunktionen irregulärer Eigenwertprobleme
• The completeness of eigenfunctions and associated functions of an ordinary differential operator with irregular-separated boundary conditions
• Differential operator with irregular splitting boundary conditions
• On a new method for solving irregular problems
• Properties of spectral expansions corresponding to non-self-adjoint differential operators.
• First and second order differentiation operators with weight functions of variable sign
• Equiconvergence theorems for differential operators
• Birkhoff regularity in terms of the growth of the norm for the Green function
• Riesz bases of root vectors of indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions. II
• Das asymptotische Verhalten der Greenschen Funktion irregulärer Eigenwertprobleme mit zerfallenden Randbedingungen
• \((C, 1)\)-summability of Fourier series in root functions of ordinary linear differential operators in a space of vector functions
• Regular and completely regular differential operators
• Die Entwicklungen nach Eigenfunktionen irregulärer Eigenwertprobleme mit zerfalleneden Randbedingungen
• Green's function for ordinary differential operators
• Die Entwicklungen nach Eigenfunktionen irregulärer Eigenwertprobleme mit zerfallenden Randbedingungen. II. (Expansion of eigenfunctions of irregular eigenvalue problems with decomposable boundary conditions. II)
• Double completeness of the system of eigenfunctions and associated functions of the Regge problem
• Zur Regularität selbstadjungierter Randwertaufgaben
• Nicht-S-hermitesche Rand- und Eigenwertprobleme
• Das Verhalten der Greenschen Matrix und der Entwicklungen nach Eigenfunktionen N-regulärer Eigenwertprobleme
• A third order irregular boundary value problem and the associated series
• On the behaviour of eigenfunction expansions in the complex domain
• An expansion theorem for eigenvalue problems with several turning points
• On the analytic behaviour of the eigenvalue of theS-matrix in the complex plane of the energy
• Eigenvalues and completeness for regular and simply irregular two-point differential operators
• Asymptotics of eigenvalues and estimate for the kernel of the resolvent in an irregular boundary value problem generated by a 2n-th order differential equation on the interval [0,a]
• Boundary value problems with eigenvalue depending boundary conditions
• On the completeness of eigenfunctions and associated functions of irregular multipoint eigenvalue-problems.
• Das asymptotische verhalten der greenschen funktion N-irregulaärer eigenwertprobleme mit zerfallenden randbedingungen
• General boundary eigenvalue problems for systems of differential equations with multiple roots of the characteristic equation
• Expansion theorems for Birkhoff-regular differential-boundary operators
• Irregular multipoint eigenvalue problems
• Expansion problems with irregular multipoint boundary conditions
• Strongly irregular boundary value problems
• Irregular boundary value problems for ordinary differential equations
• Abel-Summability of Eigenfunction Expansions of Three—Point Boundary Value Problems
• Onn-Fold Expansions for Ordinary Differential Operators
• Odd and Even Cases of Birkhoff‐Regularity
• Connection Formulas for Second Order Differential Equations with a Complex Parameter and Having an Arbitrary Number of Turning Points
• Spectral Analysis for Linear Pencils N — λP of Ordinary Differential Operators
• Regular Boundary Conditions for Ordinary Differential Operators
• A third order boundary value problem arising in aeroelastic wing theory
• A Theory for Ordinary Differential Boundary Problems of the Second Order and of the Highly Irregular Type
• Boundary eigenvalue problems for differential equations \(N\eta=\lambda P\eta\) with \(\lambda\)-polynomial boundary conditions

This page was built for publication: Irregular boundary value problems revisited