In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type ( Dn − n−1 ∑ i=1 aiD αi ) x(t) ∈ F (t, x(φ(t))), a.e. on (0, 1), I1−αnx(0) = c, αn ∈ (0, 1), where F (t, ·) is lower semicontinuous from R into R and F (·, ·) is measurable. The corresponding single-valued problem will be considered first.

a theory is presented for the dispersion relations of the nonlinear phonon-polaritons arising when phonons are coupled to the electromagnetic waves in multilayered structures of nonlinear materials. the calculations are applied to a multilayered structure consisting of a thin film surrounded by semi-infinite bounding media where each layer may have a frequency dependent dielectric function and ...

Inmany problems in analysis, dynamics, and in their applications, it is important to subdivide objects under consideration into simple pieces, keeping control of high-order derivatives. It is known that semi-algebraic sets and mappings allow for such a controlled subdivision: this is the “Ck reparametrization theorem” which is a high-order quantitative version of the well-known results on the e...

We study deformation theory for quantum integrable systems and prove several theorems concerning the Gevrey convergence and the unicity of perturbative expansions. À V.I. Arnold pour ses 70 ans.