Project information
Qualitative theory of half-linear 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 half-linear differential equation (r(t)fí(y´))´ +p(t)fí(y)=0, where fí(x) = lx]alfa-2x and a > 1, its discrete counterpart - half-linear difference equation, and other related equ ations. It is a well-known fact that there exists a striking similarity between theories of (HLDE) and Sturm-Liouville 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 (one-dimensional) case of partial differential equation with the so-called alfa-Laplacian 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
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Bounded solutions and wavefronts for discrete dynamics
Computers & Mathematics with Applications, year: 2004, volume: 47, edition: 6-7
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On certain comparison theorems for half-linear dynamic equations on time scales
Abstr, Appl. Anal., year: 2004, volume: 2004, edition: 7
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Oscillation of coupled nonlinear discrete systems
Journal of Mathematical Analysis and Applications, year: 2004, volume: 295, edition: 2
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Strongly decaying solutions of nonlinear forced discrete systems
Proceedings of the Sixth International Conference on Difference Equations, year: 2004
2003
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Half-linear 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.
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Recessive solution of half-linear second order difference equations
J. Difference Equ. Appl., year: 2003, volume: 9, edition: 1, DOI
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Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems
Dynamic Systems and Applications, year: 2003, volume: 12, edition: 1-2
2002
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Comparison theorems for linear dynamic equations on time scales
Journal of Mathematical Analysis and Applications, year: 2002, volume: 275, edition: 1, DOI
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Half-linear dynamic equations on time scales: IVP and oscillatory properties
Nonlinear Functional Analysis and Applications, year: 2002, volume: 7, edition: 3
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Nonoscillatory solutions for nonlinear discrete systems
Proceedings of Equadiff 10 (CD ROM), year: 2002