Effet tunnel pour l'équation de Schrödinger avec champ magnétique
Eigenfunctions and Nodal Sets
Eigenvalue problems of quasilinear elliptic systems on Rn.
In this paper we get the existence results of the nontrivial weak solution (λ,u) of the following eigenvalue problem of quasilinear elliptic systems-Dα (aαβ(x,u) Dβui) + 1/2 Dui aαβ(x,u)Dαuj Dβuj + h(x) ui = λ|u|p-2ui, for x ∈ Rn, 1 ≤ i ≤ N and u = (u1, u2, ..., uN) ∈ E = {v = (v1, v2, ..., vN) | vi ∈ H1(Rn), 1 ≤ i ≤ N},where aαβ(x,u) satisfy the natural growth conditions. It seems that this kind of problem has never been dealt with before.
Erratum : “Analytic properties of the resolvent for the Helmholtz operator oustide a periodic surface”
Erratum to “Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials”.
Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series.