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Generalized boundary value problems with linear growth

Valter Šeda (1998)

Mathematica Bohemica

It is shown that for a given system of linearly independent linear continuous functionals l i C n - 1 → ℝ , i = 1 , ⋯ , n , the set of all n -th order linear differential equations such that the Green function for the corresponding generalized boundary value problem (BVP for short) exists is open and dense in the space of all n -th order linear differential equations. Then the generic properties of the set of all solutions to nonlinear BVP-s are investigated in the case when the nonlinearity in the differential equation has...

Generalized differential equations in the space of regulated functions (boundary value problems and controllability)

Milan Tvrdý (1991)

Mathematica Bohemica

Boundary value problems for generalized linear differential equations and the corresponding controllability problems are dealt with. The adjoint problems are introduced in such a way that the usual duality theorems are valid. As a special case the interface boundary value problems are included. In contrast to the earlier papers by the author the right-hand side of the generalized differential equations as well as the solutions of this equation can be in general regulated functions (not necessarily...

Generalized Gaudin models and Riccatians

Aleksander Ushveridze (1996)

Banach Center Publications

The systems of differential equations whose solutions exactly coincide with Bethe ansatz solutions for generalized Gaudin models are constructed. These equations are called the generalized spectral ( 1 ) Riccati equations, because the simplest equation of this class has a standard Riccatian form. The general form of these equations is R n i [ z 1 ( λ ) , . . . , z r ( λ ) ] = c n i ( λ ) , i=1,..., r, where R n i denote some homogeneous polynomials of degrees n i constructed from functional variables z i ( λ ) and their derivatives. It is assumed that d e g ∂ k z i ( λ ) = k + 1 . The problem...

Generalized Picone's formula and forced oscillations in quasilinear differential equations of the second order

Jaroslav Jaroš, Takaŝi Kusano, N. Yoshida (2002)

Archivum Mathematicum

In the paper a comparison theory of Sturm-Picone type is developed for the pair of nonlinear second-order ordinary differential equations first of which is the quasilinear differential equation with an oscillatory forcing term and the second is the so-called half-linear differential equation. Use is made of a new nonlinear version of the Picone’s formula.

Generalized practical stability analysis of discontinuous dynamical systems

Guisheng Zhai, Anthony Michel (2004)

International Journal of Applied Mathematics and Computer Science

In practice, one is not only interested in the qualitative characterizations provided by the Lyapunov stability, but also in quantitative information concerning the system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner using the concept of practical stability. In the present paper, we give a new definition of generalized practical stability (abbreviated as GP-stability) and...

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