Qualitative theory of halflinear differential and difference equations
 Project Identification
 GP201/01/P041
 Project Period
 1/2001  1/2003
 Investor / Pogramme / Project type

Czech Science Foundation
 Postdoctoral projects
 MU Faculty or unit
 Faculty of Education
 Other MU Faculty/Unit

Faculty of Science
 prof. RNDr. Ondřej Došlý, DrSc.
In the present project there will be studied qualitative properties of the halflinear differential equation (r(t)fí(y´))´ +p(t)fí(y)=0, where fí(x) = lx]alfa2x and a > 1, its discrete counterpart  halflinear difference equation, and other related equ ations. It is a wellknown fact that there exists a striking similarity between theories of (HLDE) and SturmLiouville differential equation (which is the special case of (HLDE) for alfa = 2) that enable to use methods known from theory of linear equatio ns for investigating of (HLDE) and hereby to obtain the strong results. The study of (HLDE) is important (among others) for the following reasons: 1) Equation (HLDE) is a special (onedimensional) case of partial differential equation with the socalled alfaLaplacian which describes many physical and chemical phenomena. The results obtained in the connection with equation (HLDE) are good bases for an extension to the multidimensional case, 2) We can use the results concerning (HLDE) in the study of equ
Publications
Total number of publications: 12
2004

Bounded solutions and wavefronts for discrete dynamics
Computers & Mathematics with Applications, year: 2004, volume: 47, edition: 67

On certain comparison theorems for halflinear dynamic equations on time scales
Abstr, Appl. Anal., year: 2004, volume: 2004, edition: 7

Oscillation of coupled nonlinear discrete systems
Journal of Mathematical Analysis and Applications, year: 2004, volume: 295, edition: 2

Strongly decaying solutions of nonlinear forced discrete systems
Proceedings of the Sixth International Conference on Difference Equations, year: 2004
2003

Halflinear dynamic equations
Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, Ravi P. Agarwal, Donal O'Regan editors, year: 2003, number of pages: 56 s.

Recessive solution of halflinear second order difference equations
J. Difference Equ. Appl., year: 2003, volume: 9, edition: 1, DOI

Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems
Dynamic Systems and Applications, year: 2003, volume: 12, edition: 12
2002

Comparison theorems for linear dynamic equations on time scales
Journal of Mathematical Analysis and Applications, year: 2002, volume: 275, edition: 1, DOI

Halflinear dynamic equations on time scales: IVP and oscillatory properties
Nonlinear Functional Analysis and Applications, year: 2002, volume: 7, edition: 3

Nonoscillatory solutions for nonlinear discrete systems
Proceedings of Equadiff 10 (CD ROM), year: 2002