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Author: Vacaraş Olga Degree: doctor of physics and mathematics Speciality:  01.01.02 - Differential equations Year: 2018 Scientific advisers: Alexandru Şubă doctor habilitat, professor, Tiraspol State University Romanovski Valery doctor habilitat ın ştiinţe fizico-matematice, profesor universitar, Slovenia Institution: Institute of Mathematics and Computer Science

Status The thesis was presented on the 19 May, 2017 Approved by NCAA on the 11 May, 2018 Abstract – 0.57 Mb / in romanian Thesis CZU 517.925 1.02 Mb / in romanian 149 pages

Keywords

Summary

Field of study: qualitative theory of differential equations. The sub ject of study is the cubic system of differential equations with real coefficients.

The purpose and ob jectives: establishing the maximal multiplicity of an invariant straight line for differential polynomial systems; to give a classification of cubic systems with one, with two and with three invariant straight lines of maximal multiplicity; studying the problem of Darboux integrability for the obtained systems.

Scientific novelty and originality consists in the study of cubic systems of differential equations with non-degenerate infinity, having at most three multiple invariant straight lines (including the line at infinity) and in the establishing the maximal multiplicity of an invariant straight line for cubic systems and in the estimating the maximal algebraic multiplicity of an invariant straight line for polynomial systems of degree n, n ≥ 2.

The important scientific problem solved consists in the classification of cubic systems with one (the line at infinity), with two and with three invariant straight lines of maximal multiplicity and the construction of the perturbed cubic systems corresponding to the canonical forms in the case of the real invariant straight lines.

The theoretical significance: the obtained results in this thesis are new and are a continuation of the study of the cubic systems with invariant straight lines.

Implementation of the scientific results: the results of this thesis can be used: in the further investigations of cubic systems with invariant algebraic curves, as a support for teaching optional courses in higher education, in the study of some mathematical models which describe processes in physics, chemistry, biology, economy and others.

Oficial Reviewers

• Dumitru Cozma
  doctor habilitat, associate professor (docent)
• Victor Pricop
  doctor, associate professor (docent)

Council's Members

• Mitrofan Cioban, president
  doctor habilitat, professor
• Victor Orlov, secretary
  doctor
• Vasile Neagu, member
  doctor habilitat, professor, Moldova State University
• Mihail Popa, member
  doctor habilitat, professor, Institute of Mathematics and Computer Science
• Nicolae Vulpe, member
  doctor habilitat, professor, Institute of Mathematics and Computer Science

 Theses