Fw: new_abstracts 21 059

[Maria Odete Madeira]

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NEW ABSTRACTS (Feb 18 to Feb 25)

==================== 21-10 ====================

Oleg Safronov

Eigenvalue bounds for Schr\"odinger operators with random complex potentials

(502K, pdf)

ABSTRACT.  We consider the Schr\"odinger operator perturbed by a random complex-valued potential. For this operator,

we consider its eigenvalues situated in the unit disk. We

obtain an estimate on the rate of accumulation of these eigenvalues to the positive half-line.

http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=21-10

http://www.maia.ub.es/mp_arc-bin/mpa?yn=21-10

http://kleine.mat.uniroma3.it/mp_arc-bin/mpa?yn=21-10

==================== 21-9 ====================

Vitaly Volpert and Vitali Vougalter

Method of monotone solutions for reaction-diffusion equations

(365K, pdf)

ABSTRACT.  Existence of solutions of reaction-diffusion systems of equations in unbounded domains is studied by the Leray-Schauder (LS) method based on

the topological degree for elliptic operators in unbounded domains and on

a priori estimates of solutions in weighted spaces. We identify some reaction-diffusion systems for which there exist two subclasses of solutions separated in the function space, monotone and nonmonotone solutions. A priori estimates and existence of solutions are obtained for monotone solutions allowing to prove their existence by the LS method.

Various applications of this method are given.

http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=21-9

http://www.maia.ub.es/mp_arc-bin/mpa?yn=21-9

http://kleine.mat.uniroma3.it/mp_arc-bin/mpa?yn=21-9