ON SECOND-ORDER ALMOST-PERIODIC ELLIPTIC OPERATORS

Liouville Type Results for Periodic and Almost Periodic Elliptic Operators

The main feature of this paper concerns extensions of the Liouville theorem to the following class of elliptic equations in non-divergence form: aij(x)∂iju + bi(x)∂iu + c(x)u = 0 in R N , with c ≤ 0. We show that the Liouville property holds (that is, the space of bounded solutions has at most dimension one) if the coefficients aij , bi and c are periodic, with the same period, and it does not ...

On the Spectrum of a Class of Second Order Periodic Elliptic Differential Operators

Order Almost Dunford-Pettis Operators on Banach Lattices

By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford- Pettis and weakly limited operators. Then, we characterize Banach lat- tices E and F on which each operator from E into F t...

On a factorization of second order elliptic operators and applications

We show that given a nonvanishing particular solution of the equation (div p grad+q)u = 0, (1) the corresponding differential operator can be factorized into a product of two first order operators. The factorization allows us to reduce the equation (1) to a first order equation which in a two-dimensional case is the Vekua equation of a special form. Under quite general conditions on the coeffic...

Eigenvalue Multiplicities for Second Order Elliptic Operators on Networks Joachim

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...