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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Controllability theorem for nonlinear dynamical systems

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
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tom 22
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nr 2
225-232
EN
Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.
2
Content available remote

Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivatives

100%
Liu Y.
Nonautonomous Dynamical Systems
|
2016
|
tom 3
|
nr 1
42-84
EN
In this article, we present a new method for converting the boundary value problems for impulsive fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some existence results for solutions of a class of boundary value problems for nonlinear impulsive fractional differential systems at resonance case and non-resonance case are established respectively. Our analysis relies on the well known Schauder’s fixed point theorem and coincidence degree theory. Examples are given to illustrate main results. This paper is motivated by [Solvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Equ. 89(2011), 1-19], [Existence result for boundary value problem of nonlinear impulsive fractional differential equation at resonance, J, Appl, Math, Comput. 39(2012) 421-443] and [Solvability for a coupled system of fractional differential equations with impulses at resonance, Bound. Value Probl. 2013, 2013: 80].
3
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Some existence results for solutions of differential inclusions with retardations

100%
Erbe L., Krawcewicz W., Chen S.
Annales Polonici Mathematici
|
1991
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tom 54
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nr 3
227-239
EN
Using the topological transversality method of Granas we prove an existence result for a system of differential inclusions with retardations of the form y'' ∈ F(t,y,y',Φ(y)). The result is applied to the study of the existence of solutions to an equation of the trajectory of an r-stage rocket with retardations.
4
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Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc

100%
Mityushev V.
Annales Polonici Mathematici
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1998
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tom 68
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nr 3
227-236
EN
The conformal mapping ω(z) of a domain D onto the unit disc must satisfy the condition |ω(t)| = 1 on ∂D, the boundary of D. The last condition can be considered as a Dirichlet problem for the domain D. In the present paper this problem is reduced to a system of functional equations when ∂D is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series.
5

Some remarks on boundary value problem for differential inclusions

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1997
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tom 17
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nr 1-2
43-49
EN
Some sufficient conditions for the existence of solutions to boundary value problem for differential inclusions are given.
6
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On the Picard problem for hyperbolic differential equations in Banach spaces

88%
Sadowski A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2003
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tom 23
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nr 1
31-37
EN
B. Rzepecki in [5] examined the Darboux problem for the hyperbolic equation $z_{xy} = f(x,y,z,z_{xy})$ on the quarter-plane x ≥ 0, y ≥ 0 via a fixed point theorem of B.N. Sadovskii [6]. The aim of this paper is to study the Picard problem for the hyperbolic equation $z_{xy} = f(x,y,z,z_x,z_{xy})$ using a method developed by A. Ambrosetti [1], K. Goebel and W. Rzymowski [2] and B. Rzepecki [5].
7
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Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems

88%
Navarro E., Company R., Jódar L.
Applicationes Mathematicae
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1993-1995
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tom 22
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nr 1
11-23
EN
In this paper we consider Bessel equations of the type $t^2 X^{(2)}(t) + t X^{(1)}(t) + (t^2 I - A^2)X(t) = 0$, where A is an n$\times$n complex matrix and X(t) is an n$\times$m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.
8
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Systems of differential inclusions in the absence of maximum principles and growth conditions

75%
Tisdell C.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2006
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tom 26
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nr 1
129-141
EN
This article investigates the existence of solutions to second-order boundary value problems (BVPs) for systems of ordinary differential inclusions. The boundary conditions may involve two or more points. Some new inequalities are presented that guarantee a priori bounds on solutions to the differential inclusion under consideration. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow the treatment of systems of BVPs in the absence of maximum principles and growth conditions. The results are also new for differential equations involving Carathéodory or even continuous right-hand sides.
9
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Qualitative behavior of a class of second order nonlinear differential equations on the halfline

75%
Staněk S.
Annales Polonici Mathematici
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1993
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tom 58
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nr 1
65-83
EN
A differential equation of the form (q(t)k(u)u')' = F(t,u)u' is considered and solutions u with u(0) = 0 are studied on the halfline [0,∞). Theorems about the existence, uniqueness, boundedness and dependence of solutions on a parameter are given.
10
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Boundary Value Problems for Differential Equations with Fractional Order and Nonlinear Integral Conditions

75%
Benchohra M., Hamani S.
Commentationes Mathematicae
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2009
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tom 49
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nr 2
EN
In this paper, we shall establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential equations involving the Caputo fractional derivative and nonlinear integral conditions.
11
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Nonnegative solutions of a class of second order nonlinear differential equations

75%
Staněk S.
Annales Polonici Mathematici
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1992
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tom 57
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nr 1
71-82
EN
A differential equation of the form (q(t)k(u)u')' = λf(t)h(u)u' depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.
12
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Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory

63%
Djebali S., Ouahab A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2010
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tom 30
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nr 1
23-49
EN
In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are provided.
13
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Fourier-like methods for equations with separable variables

51%
Przeworska-Rolewicz D.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2009
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tom 29
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nr 1
19-42
EN
It is well known that a power of a right invertible operator is again right invertible, as well as a polynomial in a right invertible operator under appropriate assumptions. However, a linear combination of right invertible operators (in particular, their sum and/or difference) in general is not right invertible. It will be shown how to solve equations with linear combinations of right invertible operators in commutative algebras using properties of logarithmic and antilogarithmic mappings. The used method is, in a sense, a kind of the variables separation method. We shall obtain also an analogue of the classical Fourier method for partial differential equations. Note that the results concerning the Fourier method are proved under weaker assumptions than these obtained in [6] (cf. also [7, 8, 11]).
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