On semilinear elliptic eigenvalue problem with eigenparameter in the boundary conditions.
On some new spectral estimates for Schrödinger-like operators
We prove the analog of the Cwikel-Lieb-Rozenblum estimate for a wide class of second-order elliptic operators by two different tools: Lieb-Thirring inequalities for Schrödinger operators with matrix-valued potentials and Sobolev inequalities for warped product spaces.
On some Schrödinger operators with a singular complex potential
On stability of classes of Lipschitz mappings generated by compact sets of linear mappings.
On the Abel basis property of the system of root vector-functions of degenerate elliptic differential operators with singular matrix coefficients.
On the Aharonov-Casher formula for different self-adjoint extensions of the Pauli operator with singular magnetic field.
On the existence and uniqueness of solutions for an incomplete second-order abstract Cauchy problem
We prove existence and uniqueness of classical solutions for an incomplete second-order abstract Cauchy problem associated with operators which have polynomially bounded resolvent. Some examples of differential operators to which our abstract result applies are also included.
On the Exponential Bound of the Cutoff Resolvent
A simpler proof of a result of Burq [1] is presented.
On the Fröhlich-Spencer-Estimate in the theory of anderson localization.
On the Functional Dimension of Solution Spaces of Hypoelliptic Partial Differential Operators.
On the minimal space of surjectivity question for linear transformations on vector spaces with applications to surjectivity of differential operators on locally convex spaces.
On the principal eigenvalue of elliptic operators in and applications
Two generalizations of the notion of principal eigenvalue for elliptic operators in are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures.
On the problem of convergence of a bounded-below sequence of symmetric forms for the Schrödinger operators
On the range of elliptic operators discontinuous at one point
Let be a second order, uniformly elliptic, non variational operator with coefficients which are bounded and measurable in () and continuous in . Then, if is a bounded domain, we prove that is dense in for any .
On the range of nonlinear operators with linear asymptotes which are not invertible
On the Schrödinger equation in L...spaces.
On the second eigenvalue of a Hardy-Sobolev operator.
On the singularities of solutions of partial differential equations with constant coefficients
On the solution -dimensional of the product operator and diamond Bessel operator.
On the solutions of nonlinear initial-boundary value problems.