We consider a class of eigenvalue problems involving coefficients changing sign on the domain of interest. We describe the main spectral properties of these problems according to the features of the coefficients. Then, under some assumptions on the mesh, we explain how one can use classical finite element methods to approximate the spectrum as well as the eigenfunctions while avoiding spurious ...

We investigate the properties of the operator ∆(σ∆·) : H0(Ω) → H−2(Ω), where σ is a given parameter whose sign can change on the bounded domain Ω. Here, H0(Ω) denotes the subspace of H2(Ω) made of the functions v such that v = ν · ∇v = 0 on ∂Ω. The study of this problem arises when one is interested in some configurations of the Interior Transmission Eigenvalue Problem. We prove that ∆(σ∆·) : H...

Via variational methods, we study multiplicity of solutions for the problem    −∆u = λb(x)|u|q−2u + a u + g(x, u) in Ω , u = 0 on ∂Ω . where a simple example for g(x, u) is |u|p−2u; here a, λ are real parameters, 1 < q < 2 < p ≤ 2∗ and b(x) is a function in a suitable space L. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any λ > 0, and a...

We investigate differential electron momentum distributions in nonsequential double ionization with linearly polarized, few-cycle pulses, using a classical model based on a laser-assisted inelastic (e(-),2e(-)) rescattering mechanism. These yields, as functions of the momentum components parallel to the laser polarization, are highly asymmetric and strongly influenced by the phase difference be...