Continuous spectrum for a class of nonhomogeneous differential operators

ar X iv : 0 71 1 . 09 04 v 1 [ m at h . A P ] 6 N ov 2 00 7 A continuous spectrum for nonhomogeneous differential operators in Orlicz - Sobolev spaces ∗

We study the nonlinear eigenvalue problem−div(a(|∇u|)∇u) = λ|u|q(x)−2u in Ω, u = 0 on ∂Ω, where Ω is a bounded open set in R with smooth boundary, q is a continuous function, and a is a nonhomogeneous potential. We establish sufficient conditions on a and q such that the above nonhomogeneous quasilinear problem has continuous families of eigenvalues. The proofs rely on elementary variational ar...

Continuous spectrum of a fourth order nonhomogeneous differential operators with variable exponent

The study of differential equations and variational problems with variable exponent has been a new and interesting topic. Its interest is widely justified with many physical examples, such as nonlinear elasticity theory, electrorheological fluids, etc. (see [1, 2]). It also has wide applications in different research fields, such as image processing model (see e.g. [3,4]), stationary thermorheo...

Sandwich-type theorems for a class of integral operators with special properties

In the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

properties of M−hyoellipticity for pseudo differential operators

In this paper we study properties of symbols such that these belong to class of symbols sitting insideSm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudodifferential operators for which define base on this class of symbols. Also we consider maxi...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators