SVIBOR - Project code: 1-01-113

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Project code: 1-01-113

THE QUALITATIVE ANALYSIS OF SOME DIFFERENTIAL EQUATIONS

Main researcher: VRDOLJAK, BOŽO (53341)

Assistants

VUČIČIĆ, TANJA (105526)
HENČ, DAMIR (95145)

Type of research: basic
Duration from: 01/01/91. to 12/31/94.

Papers on project (total): 32
Papers on project quoted in Current Contents: 4

Institution name: Građevinski fakultet, Split (83)
Department/Institute: Department of Mathematics and Physics
Address: Matice hrvatske 15
City: 21000 - Split, Croatia

Communication: Phone: 385 (0)21 52-33-33; Fax: 385 (0)21 52-41-62; E-mail: vrdoljak@cigla.gradst.hr

Summary: The qualitative analysis of solutions of certain higher order nonlinear ordinary differential equations, systems of linear and nonlinear differential equations, dynamical systems and radially symmetric solutions of some nonlinear partial differential equations, in particular semilinear elliptic equations and nonlinear Schrodinger equation, in a ball and in an annulus in Rn, is studied. The analysis includes certain problems which have been considered by other authors by employing different methods. The existence, behaviour, stability and approximation of a bounded as well as unbounded solutions, with initial and boundary conditions, on a bounded and unbounded regions, are established. The errors of the approximation of the solutions, whose existence are established, are defined by the corresponding functions which can be either sufficiently or arbitrarily small. The qualitative analysis theory of differential equations and the corresponding topological methods are used.

Keywords: Ordinary differential equations, partial differential equations, dynamical systems, semilinear elliptic equations, Schrodinger equation, qualitative analysis, retraction method, initial value problems, boundary value problems, radial solutions.

Research goals: The objective of the investigations is to perform a precise qualitative analysis from the standpoint of the existence, behaviour, stability and approximation of solutions of the respective linear and nonlinear ordinary differential equations of higher order, of the systems of linear and nonlinear differential equations, dynamical systems and radial solutions of some partial differential equations. Various forms of semilinear elliptic equations and Schrodinger equation in a ball and in an annulus in Rn, with finite and infinite radius, particularly to consider. The analysis includes certain problems which have been considered by other authors by employing different methods. These problems are important in mathematics as well as in other scientific disciplines. The results to obtain by employing original procedures and to present a significant contribution to the theory of differential equations, and especially to qualitative analysis of differential equations.

COOPERATION - INSTITUTIONS

Name of institution: Matematički odjel Prirodoslovno-matematičkog fakulteta Sveučilišta u Zagrebu
Type of institution: University/Faculty
Type of cooperation: Occasional exchange of information
City: 10000 - Zagreb, Croatia
Name of institution: Građevinski fakultet Sveučilišta u Zagrebu
Type of institution: University/Faculty
Type of cooperation: Occasional exchange of information
City: 10000 - Zagreb, Croatia
Name of institution: Fakultet prirodoslovno-matematičkih znanosti i odgojnih područja u Splitu
Type of institution: University/Faculty
Type of cooperation: Joint project
City: 21000 - Split, Croatia
Name of institution: Prirodno-matematički fakultet Univerziteta u Sarajevu
Type of institution: University/Faculty
Type of cooperation: Occasional exchange of information
City: Sarajevo, Bosna i Hercegovina
Name of institution: Inštitut za matematiko, fiziko in mehaniko Univerze v Ljubljana
Type of institution: University/Faculty
Type of cooperation: Occasional exchange of information
City: Ljubljana, Slovenija
Name of institution: Fakultet elektrotehnike, strojarstva i brodogradnje Sveučilišta u Splitu
Type of institution: University/Faculty
Type of cooperation: Occasional exchange of experts
City: 21000 - Split, Croatia
Name of institution: Prirodno-matematički fakultet Univerziteta Kiril i Metodij
Type of institution: University/Faculty
Type of cooperation: Occasional exchange of information
City: Skopje, Makedonija
Name of institution: Bolyai Institute
Type of institution: State institute
Type of cooperation: Occasional exchange of information
City: Szeged, Hungary
Name of institution: Department of Mathematics, Faculty of Mechanical Engineering, Budapest University of Technology
Type of institution: University/Faculty
Type of cooperation: Occasional exchange of information
City: Budapest, Hungary
Name of institution: Department of Mathematics, Technical University of Brno
Type of institution: University/Faculty
Type of cooperation: Occasional exchange of information
City: Brno, Czech Republic
Name of institution: Gesellschaft fur Angewandte Mathematik und Mechanik
Type of institution: International organization
Type of cooperation: Occasional exchange of information
City: Regenzburg, Germany
Name of institution: Society for Industrial and Applied Mathematics
Type of institution: International organization
Type of cooperation: Occasional exchange of information
City: Philadelphia, USA
Name of institution: American Mathematical Society
Type of institution: International organization
Type of cooperation: Occasional exchange of information
City: Providence, USA

Other information about the project.


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Last update: 10/09/95
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