Tensor products of linear operators in locally convex spaces
The Algebraic Multiplicity of Eigenvalues and the Evans Function Revisited
This paper is related to the spectral stability of traveling wave solutions of partial differential equations. In the first part of the paper we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an abstract operator on a Hilbert space, and the algebraic multiplicity of the eigenvalue of the corresponding Birman-Schwinger type operator pencil. In the second part of the paper we apply this result...
The Cauchy problem for an inclusion in Banach spaces and distribution spaces.
The dependence of the eigenvalues of the Sturm-liouville problem on boundary conditions
The division method for subspectra of self-adjoint differential vector-operators.
The existence of bounded solutions for differential equations in Hilbert spaces
The existence of bounded solutions for equations x' = A(t)x + r(x,t) is proved, where the linear part is exponentially dichotomic and the nonlinear term r satisfies some weak conditions.
The Friedrichs extension of certain singular differential operators. II.
The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points
The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0...
The inverse spectral problem for the Sturm-Liouville operators with discontinuous coefficients.
The operator equation AX - XB = C with unbounded operators A and B and related abstract Cauchy problems.
The ratio of eigenvalues of the Dirichlet eigenvalue problem for equations with one-dimensional -Laplacian.
The spectra of general differential operators in the direct sum spaces
In this paper, the general ordinary quasi-differential expression of -th order with complex coefficients and its formal adjoint on any finite number of intervals , , are considered in the setting of the direct sums of -spaces of functions defined on each of the separate intervals, and a number of results concerning the location of the point spectra and the regularity fields of general differential operators generated by such expressions are obtained. Some of these are extensions or generalizations...
Théorèmes taubériens et théorie spectrale
Théorie de Galois -adique
Three methods for the study of semilinear equations at resonance
Three methods for the study of the solvability of semilinear equations with noninvertible linear parts are compared: the alternative method, the continuation method of Mawhin and a new perturbation method [22]-[27]. Some extension of the last method and applications to differential equations in Banach spaces are presented.
Topological -adic vector spaces and index theory
Trace Formulas of Gelfand--levitan Type