Potential flows
Potential Theory for Schrödinger operators on finite networks.
We aim here at analyzing the fundamental properties of positive semidefinite Schrödinger operators on networks. We show that such operators correspond to perturbations of the combinatorial Laplacian through 0-order terms that can be totally negative on a proper subset of the network. In addition, we prove that these discrete operators have analogous properties to the ones of elliptic second order operators on Riemannian manifolds, namely the monotonicity, the minimum principle, the variational treatment...
Power bounded and exponentially bounded matrices
The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.
Power bounded prolongations and Picard-Lindelöf iteration.
Power function solutions of iterative functional differential equations.
Power Series Solutions of Algebraic Differential Equations.
Power series techniques for a special Schrödinger operator and related difference equations.
Poznámka k aplikacím Laplaceovy transformace na abstraktní diferenciální rovnice parabolického typu
Poznámka k integrování některých differenciálních rovnic lineárních
Poznámka k otázce o oscilačních vlastnostech řešení diferenciální rovnice
Poznámka o jistých nelineárních diferenciálních rovnicích 3. a 4. řádu
Poznámka o postupných aproximacích řešení obyčejné diferenciální rovnice
Poznámka o řešení rovnice , jejíž jedno partikulární řešení je derivací druhého
Poznámky o charakteristické rovnici jisté transformace
Practical -stability behavior of time-varying nonlinear systems
We deal with the problem of practical uniform -stability for nonlinear time-varying perturbed differential equations. The main aim is to give sufficient conditions on the linear and perturbed terms to guarantee the global existence and the practical uniform -stability of the solutions based on Gronwall’s type integral inequalities. Several numerical examples and an application to control systems with simulations are presented to illustrate the applicability of the obtained results.
Practical Lyapunov stability criteria for differential algebraic equations
Practical method for solving differential equations and their systems bu means of Taylor series
Practical persistence for differential delay models of population interactions.
Practical Stability in Terms of Two Measures for Hybrid Dynamic Systems
We study hybrid dynamic systems on time scales. Using Lyapunov-like functions, we obtain sufficient conditions for practical stability and strict practical stability in terms of two measures for hybrid dynamic systems on time scales.
Practice of operator relationships in symbolical calculus.