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Author: Andrei Perjan Degree: doctor habilitat of physics and mathematics Speciality:  01.01.02 - Differential equations Year: 2009 Institution: Moldova State University Scientific council: DH 30-01.01.02-27.03.08 Moldova State University

Status The thesis was presented on the 5 December, 2008 Approved by NCAA on the 26 February, 2009 Abstract – 0.37 Mb / in romanian Thesis CZU 517.956 1.27 Mb / in romanian 244 pages

Keywords

Summary

In the thesis we investigate the singularly perturbed problems for the systems of differential equations of the first order, and also for the second order semilinear differential equations in Hilbert spaces.

Theorems on existence of singular limits of solutions to the singularly perturbed Cauchy problem for systems of nonlinear differential equations in Hilbert spaces, and also for semilinear differential equations of the second order with lipschitzian, or local lipschitzian and monotone nonlinearities are established. Also, we proved theorems on the approximations of the solutions to the Cauchy problem of the first order semilinear equations in Hilbert spaces with lipschitzian, or local lipschitzian and monotone nonlinearities by solutions to the singularly perturbed Cauchy problem for the second order equations.

The thesis is written in Romanian.

Oficial Reviewers

• Grebenicov Eugen
  doctor habilitat în ştiinţe fizico-matematice, profesor universitar, Centrul de Calcul al Academiei de Ştiinţe a Federaţiei Ruse (Moscova, Federaţia Rusă)
• Vrabie Ioan
  doctor în matematică, profesor universitar, Universitatea „Al. I. Cuza” (Iaşi, România)
• Barbu Viorel
  doctor în matematică, prof. univ., academician al Academiei Române, Filiala Iaşi a Academiei Române, Iaşi, România

Council's Members

• Nicolae Jitaraşu, president
  doctor habilitat, professor
• Valeriu Guţu, secretary
  doctor, associate professor (docent)
• Vasile Glavan , member
  doctor habilitat, professor
• Cârjă Ovidiu, membru
  doctor în matematică, profesor universitar, Universitatea „Al. I. Cuza”(Iaşi, România)
• Tiba Dan, membru
  doctor în matematică,cercetător ştiinţific gradul I, Institutul de Matematică „Simion Stoilow” al Academiei Române, Bucureşti, Romania

 Theses