The eigenvalue problem for a singular quasilinear elliptic equation.
The eigenvalue problem for the -Laplacian-like equations.
The eigenvalue problem with conductivity boundary conditions
The Eikonal approximation and the asymptotics of the total scattering cross-section for the Schrödinger equation
The error estimates for the infinite element method for eigenvalue problems
The Essential Spectrum of Elliptic Systems of Mixed Order.
The essential spectrum of relativistic multi-particle operators
The essential spectrum of relativistic one-electron ions in the Jansen-Hess model.
The Existence of Wave Operators in Scattering Theory.
The first eigenvalue for the -Laplacian operator.
The first eigenvalue of -Laplacian systems with nonlinear boundary conditions.
The gaps in the spectrum of the Schrödinger operator
We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain Ω of a submanifold M in with boundary ∂Ω, which generalize many existing inequalities for the Laplacian on a bounded domain of a Euclidean space. We also establish similar inequalities for a closed minimal submanifold in the unit sphere, which generalize and improve Yang-Yau’s result.
The generalized Morawetz problem for Lavrent'ev-Bitsadze equation with spectral parameter.
The integral equation methods for the perturbed Helmholtz eigenvalue problems.
The inverse -body problem. A geometrical approach
The Lane-Emden Function and Nonlinear Eigenvalues Problems
We consider a semilinear elliptic eigenvalues problem on a ball of and show that all the eigenfunctions and eigenvalues, can be obtained from the Lane-Emden function.
The Laplace-Beltrami operator in almost-Riemannian Geometry
We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear.Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields become collinear) and the...
The laplacian operator on a Riemann surface
The laplacian operator on a Riemann surface, II
The laplacian operator on a Riemann surface, III