We focus on eventually non-linear abstract Cauchy problems with a generalized fractional derivative in time. First we prove local existence and uniqueness result, then Grönwall inequality. Before addressing the inequality, study some properties of eigenvalues eigenfunctions derivatives. Finally, consequences

We present some general bounds for the algebraic and geometric multiplicity of eigenvalues of second order elliptic operators on finite networks under continuity and weighted Kirchhoff flow conditions at the vertices. In particular the algebraic multiplicity of an eigenvalue is shown to be strictly bounded from above by the number of vertices if there are no eigenfunctions vanishing in all node...

In this paper, for a family of second-order elliptic equations with rapidly oscillating periodic coefficients and potentials, we are interested in the $H^1$ convergence rates Dirichlet eigenvalues bounds normal derivatives eigenfunctions. The rely on correctors first-order corrector potentials. And bound results an $O(\varepsilon)$ estimate solutions condition.

Eigenfunctions and eigenvalues of the free magnetic Schrödinger operator, describing a spinless particle confined to an infinite layer of fixed width, are discussed in detail. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space. Four different classes of temporally stable coherent states associated to the operator are presented. The first two classes are derived ...