Boundary problems for ordinary differential equations with parameter in the boundary conditions

From MaRDI portal
Publication:1086724

DOI10.1007/BF01084754zbMath0609.34019OpenAlexW2060503176MaRDI QIDQ1086724

A. A. Shkalikov

Publication date: 1986

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01084754




Related Items (91)

Boundary stabilization for a star-shaped network of variable coefficients strings linked by a point massExpansion of solution in terms of generalized eigenfunctions for a hyperbolic system with static boundary conditionOperator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusionsOn Dirac operator with boundary and transmission conditions depending Herglotz-Nevanlinna type functionInverse problem for quasi-periodic differential pencils with jump conditions inside the intervalAn inverse problem for Sturm-Liouville operators with non-separated boundary conditions containing the spectral parameterExponential stability and spectral analysis of the pendulum system under position and delayed position feedbacksOn fundamental systems for differential equations of Kamke typeResolvent growth and Birkhoff-regularityHalf-inverse Sturm-Liouville problem with boundary and discontinuity conditions dependent on the spectral parameterOn the completeness of root vectors generated by systems of coupled hyperbolic equationsOn the completeness and minimality of the derived chains of eigen- and associated functions of boundary eigenvalue problems nonlinearly dependant on the parameterSpectral properties of a beam equation with eigenvalue parameter occurring linearly in the boundary conditionsRecovery of the \(m\)-function from spectral data for generalized Sturm-Liouville problemsMultiple completeness of the root functions for a certain class of ordinary differential pencils with constant coefficientsMultiple completeness of the root functions for a certain class of pencils of ordinary differential operatorsBasis properties in \({L}_{p}\) of root functions of Sturm-Liouville problem with spectral parameter-dependent boundary conditionsOptimal energy decay for a nonhomogeneous flexible beam with a tip massConvergence of eigenfunction expansions for a boundary value problem with spectral parameter in the boundary conditions. IMultiple completeness of the root functions for a certain class of pencils of ordinary differential operators with constant coefficientsStability of an interconnected system of euler−bernoulli beam and heat equation with boundary couplingOn the exponential stability of Beck's problem on a star-shaped graphA Numerical Study for a Flexible Euler-Bernoulli Beam with a Force Control in Velocity and a Moment Control in Rotating VelocityExponential stability of two strings under joint damping with variable coefficientsInverse problems for discontinuous Dirac operator with eigenparameter dependent boundary and transmission conditionsExponential stability and spectral analysis of the inverted pendulum system under two delayed position feedbacksKamke Problems. Properties of the EigenfunctionsThe spectral properties of a two-term fourth-order operator with a spectral parameter in the boundary conditionRIESZ BASIS PROPERTY AND EXPONENTIAL STABILITY FOR A DAMPED SYSTEM AND CONTROLLED DYNAMICALLYThe uniqueness of the solution of an initial boundary value problem for a hyperbolic equation with a mixed derivative and a formula for the solutionAsymptotics of the eigenvalues of a two-term fourth-order operator with boundary conditions dependent on the spectral parameterInverse spectral problems for differential operators with non-separated boundary conditionsSpectral analysis of an even order differential operator with square integrable potentialCompleteness of the system of generalized eigenfunctions for a Bessel-type differential operator\( L_2\)-small ball asymptotics for Gaussian random functions: a surveyOn quantum star graphs with eigenparameter dependent vertex conditions\(L_2\)-small ball asymptotics for a family of finite-dimensional perturbations of Gaussian functionsOn the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedbackExponential stability and spectral analysis of a delayed ring neural network with a small-world connectionDivergence of spectral decompositions of Hill operators with two exponential term potentialsA new approach to asymptotic formulas for eigenfunctions of discontinuous non-selfadjoint Sturm-Liouville operatorsMultiple expansions in series of eigen- and associated functions of boundary eigenvalue problems nonlinearly dependent on the spectral parameter. IExponential stabilization of variable coefficient wave equations in a generic tree with small time-delays in the nodal feedbacksStability and regularity transmission for coupled beam and wave equations through boundary weak connectionsAsymptotic stability and Riesz basis property for tree-shaped network of stringsUnnamed ItemDynamic behavior of a one-dimensional wave equation with memory and viscous dampingStabilisation uniforme d'une équation des poutres d'Euler-Bernoulli. (Uniform stabilization of an Euler-Bernoulli beam equation).On Basis Property of Root Functions for a Class of the Second Order Differential OperatorsA uniqueness result for differential pencils with discontinuities from interior spectral dataAsymptotic analysis of solutions of ordinary differential equations with distribution coefficientsOn the completeness of root vectors of a certain class of differential operatorsEasy test for stability of laminated beams with structural damping and boundary feedback controlsComparison of direct and perturbation approaches to analysis of infinite-dimensional feedback control systemsSome properties of eigenfunctions for the equation of vibrating beam with a spectral parameter in the boundary conditionsStabilization of a one-dimensional dam-river system: nondissipative and noncollocated caseStabilization of the Euler-Bernoulli equation via boundary connection with heat equationUnnamed ItemInverse problems for non-selfadjoint quasi-periodic differential pencilsIrregular boundary value problems revisitedDiscontinuous Sturm-Liouville problems with eigenvalue dependent boundary conditionCriteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operatorsInverse problems for Sturm–Liouville operators with interior discontinuities and boundary conditions dependent on the spectral parameterBoundary eigenvalue problems for differential equations \(N\eta=\lambda P\eta\) with \(\lambda\)-polynomial boundary conditionsThe expansion of a semigroup and a Riesz basis criterionRiesz basis property and stability of planar networks of controlled stringsA general trace formula for a differential operator on a segment with zero order coefficient perturbed by a finite signed measureBasis properties of a fourth order differential operator with spectral parameter in the boundary conditionRiesz basis for strongly continuous groupsStabilisation d'une poutre. Étude du taux optimal de décroissance de l'énergie élastiqueOn the \(C_{0}\)-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beamOn the spectral problem arising in the mathematical model of bending vibrations of a homogeneous rodProperties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial loadOn eigenfunction expansions for a class of irregular quadratic pencils of second-order differential operatorsDISCONTINUOUS STURM-LIOUVILLE PROBLEMS INVOLVING AN ABSTRACT LINEAR OPERATORDynamic behavior of a heat equation with memoryOscillation properties for the Dirac equation with spectral parameter in the boundary conditionNonselfadjoint spectral problems for linear pencils \(N- \lambda P\) of ordinary differential operators with \(\lambda\)-linear boundary conditions: Completeness resultsRiesz Basis Generation of Abstract Second-Order Partial Differential Equation Systems with General Non-Separated Boundary ConditionsEXPONENTIAL STABILISATION OF A TREE-SHAPED NETWORK OF STRINGS WITH VARIABLE COEFFICIENTSExponential stabilization of an Euler-Bernoulli beam equation with variable coefficientsOn the uniform convergence of Fourier series expansions in the system of eigenfunctions of the equation of a vibrating rod at one end of which the mass is concentratedA practical method for recovering Sturm–Liouville problems from the Weyl functionOn degenerate boundary conditions and finiteness of the spectrum of boundary value problemsLinear operator pencils \(A-\lambda B\) with discrete spectrumHidden symmetries in non-self-adjoint graphsSturm--Liouville problems with boundary conditions rationally dependent on the eigenparameter. IIRecovering nonselfadjoint differential pencils with nonseparated boundary conditionsGeneralized eigenvectors of linear operators and biorthogonal systemsStrongly definitizable linear pencils in Hilbert spaceSpectral properties of a fourth order eigenvalue problem with spectral parameter in the boundary conditions



Cites Work


This page was built for publication: Boundary problems for ordinary differential equations with parameter in the boundary conditions