Structure of eigenvalues of multi-point boundary value problems.
Sturm-Liouville operator with general boundary conditions.
Sturm-Liouville systems are Riesz-spectral systems
The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.
Sufficient conditions for functions to form Riesz bases in and applications to nonlinear boundary-value problems.
Sur le spectre de quelques opérateurs et les variétés de Jacobi
Sur l'inégalité de Sobolev logarithmique des opérateurs de Laguerre à petit paramètre
Symmetric subspaces related to certain eigenvalue problems
The analysis of contour integrals.
The Approximation of Generalized Turning Points by Projection Methods with Superconvergence to the Critical Parameter.
The basis property in of the boundary value problem rationally dependent on the eigenparameter
We consider a Sturm-Liouville operator with boundary conditions rationally dependent on the eigenparameter. We study the basis property in of the system of eigenfunctions corresponding to this operator. We determine the explicit form of the biorthogonal system. Using this we establish a theorem on the minimality of the part of the system of eigenfunctions. For the basisness in L₂ we prove that the system of eigenfunctions is quadratically close to trigonometric systems. For the basisness in ...
The dependence of the eigenvalues of the Sturm-liouville problem on boundary conditions
The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems
Let be a -contraction on a Banach space and let be an almost -contraction, i.e. sum of an -contraction with a continuous, bounded function which is less than in norm. According to the contraction principle, there is a unique element in for which If moreover there exists in with , then we will give estimates for Finally, we establish some inequalities related to the Cauchy problem.
The distribution of nonprincipal eigenvalues of singular second-order linear ordinary differential equations.
The division method for subspectra of self-adjoint differential vector-operators.
The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian
We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: , x’(t), x’(τ(t))) = 0, t ∈ [0,1]; t ≤ 0; , t ≥ 1. An existence result is obtained with the help of the Leray-Schauder degree theory, with no restriction on the damping forces d/dt grad F(x).
The Fučík spectra for multi-point boundary-value problems.
The HELP inequality for Hamiltonian systems.
The inverse problem at fixed energy for finite range complex potentials
The inverse spectral problem for the Sturm-Liouville operators with discontinuous coefficients.
The mixed problem for a degenerate operator equation.