In this paper, we establish a kind of splitting theorem for the eigenvalues of a specific family
of operators on the base of a warped product. As a consequence, we prove a density …

We show that the complex absorbing potential (CAP) method for computing scattering
resonances applies to an abstractly defined class of black box perturbations of the Laplacian …

Abstract Let (SD Ω) be the Stokes operator defined in a bounded domain Ω of R 3 with
Dirichlet boundary conditions. We prove that, generically with respect to the domain Ω with C …

In this work we show that the eigenvalues of the Dirichlet problem for the biharmonic
operator are generically simple in the set of ℤ2‐symmetric regions of ℝn, n⩾ 2, with a …

We show that all resonances in Dirichlet obstacle scattering (in $\mathbb {C} $ in odd
dimensions and in the logarithmic cover of $\mathbb {C}\setminus\{0\} $ in even dimensions) …

We consider an analytic family of Riemannian metrics on a compact smooth manifold $ M $.
We assume the Dirichlet boundary condition for the $\eta $-Laplacian and obtain Hadamard …

Scattering resonances are the analogues of eigenvalues for problems on non-compact
domains. The real part and imaginary part of the resonances capture the rates of oscillation …

Our main result is that for any bounded smooth domain Ω⊂ ℝ n there exists a positive-
weight function w and an interval I such that for λ∈ I and Δ 2 u= λ w u+ f in Ω with u=∂∂ ν …

In this work, we show that the eigenvalues of the problem are generically simple in the set of
C4 regular regions of Rn, n≥ 2. In fact, we prove that there exists a residual set of regions …

Generic Simplicity for the Solutions of a Nonlinear Plate Equation Page 1 Progress in Nonlinear
Differential Equations and Their Applications, Vol. 66, 443–463 c© 2005 Birkhäuser Verlag …