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Bounded oscillation for a class of even order neutral difference equations

100%

Lin X. , Shen J.

Fasciculi Mathematici

2002

tom Nr 33

37-47

We investigate bounded oscillation for the even order neutral delay difference equation delta'' (x(n) -cx(n-m) = pn(x-k), where u is even. The sufficient conditions obtained in this paper improve and generalize the results in related literature.

Asymptotic behavior of solutions of discrete Volterra equations

100%

Migda J. , Migda M.

Opuscula Mathematica

2016

tom Vol. 36, no. 2

265--278

We consider the nonlinear discrete Volterra equations of non-convolution type [formula] We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior, especially asymptotically polynomial and asymptotically periodic solutions. We use o(ns), for a given nonpositive real s, as a measure of approximation. We also give conditions under which all solutions are asymptotically polynomial.

On the bounds for mean-values of solutions to certain third-order non-linear differential equations

100%

Afuwape A. U. , Adesina O. A.

Fasciculi Mathematici

2005

tom Nr 36

5-14

In this paper, the issue of bounds for the mean-values of solutions of some third-order differential equations with non-linear terms is considered. It is shown that these bounds are independent of the solutions for the considered equations.

On positive solutions of a class of second order nonlinear differential equations on the halfline

86%

Staněk S.

Annales Polonici Mathematici

1995

tom 62

nr 2

123-142

The differential equation of the form $(q(t)k(u)(u')^a)' = f(t)h(u)u'$, a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u'(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.

Nonnegative solutions of a class of second order nonlinear differential equations

86%

Staněk S.

Annales Polonici Mathematici

1992

tom 57

nr 1

71-82

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.

Multivalued linear operators and differential inclusions in Banach spaces

86%

Baskakov A. , Obukhovskii V. , Zecca P.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2003

tom 23

nr 1

53-74

In this paper, we study multivalued linear operators (MLO's) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the Hille-Yosida condition. Then we describe the generalized semigroups induced by MLO's. We present a criterion for an MLO to be a generator of a generalized semigroup in an arbitrary Banach space. Finally, we obtain some existence results for differential inclusions with MLO's and various types of multivalued nonlinearities. As a consequence, we give theorems on the existence of local, global and bounded solutions of the Cauchy problem for degenerate differential inclusions.

Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)

86%

Mikołajski J. , Schmeidel E.

Opuscula Mathematica

2006

tom Vol. 26, no. 2

343-349

Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.

Qualitative behavior of a class of second order nonlinear differential equations on the halfline

86%

Staněk S.

Annales Polonici Mathematici

1993

tom 58

nr 1

65-83

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.

A nonstandard Volterra integral equation on time scales

72%

Reinfelds A. , Christian S.

Demonstratio Mathematica

2019

tom Vol. 52, nr 1

503--510

This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.