On positive solutions of some periodic parabolic eigenvalue problem with a weight function
On principal eigenvalues for periodic parabolic Steklov problems.
On quasilinear elliptic equations in domains with conical boundary points.
On reaction-diffusion systems.
On resonant scattering for time-periodic perturbations
On Riesz means of eigenfunction expansions for the Kohn-Laplacian.
On Selberg's Eigenvalue Conjecture.
On semilinear elliptic eigenvalue problem with eigenparameter in the boundary conditions.
On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case
We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.
On some elliptic transmission problems
Boundary value problems for second order linear elliptic equations with coefficients having discontinuities of the first kind on an infinite number of smooth surfaces are studied. Existence, uniqueness and regularity results are furnished for the diffraction problem in such a bounded domain, and for the corresponding transmission problem in all of . The transmission problem corresponding to the scattering of acoustic plane waves by an infinitely stratified scatterer, consisting of layers with physically...
On some linear eigenvalue problems for strongly elliptic systems with an indefinite weight matrix function
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 nonlinear partial differential equations involving the 1-Laplacian
Let be a smooth bounded domain in and let . We prove here the existence of nonnegative solutions in , to the problemwhere denotes the unit outer normal to , and denotes some function defined as:Moreover, we prove the tight convergence of towards one of the first eingenfunctions for the first Laplacian Operator on when goes to .
On some properties of eigenvalues and eigenfunctions of certain differential equations of the fourth order
On Space-Time Means Everywhere Defined Scattering Operators for Nonlinear Klein-Gordon Equations.
On spectral approximation. Part 1. The problem of convergence
On spectral approximation. Part 2. Error estimates for the Galerkin method
On spectral projections of elliptic operators
On spectral properties of adiabatically perturbed Schroedinger operators with periodic potentials
On spectral properties of the Laplace operator via boundary perturbation.