Z. Došlá - Academia.edu (original) (raw)

Papers by Z. Došlá

This is the paper written in memory of outstanding Czech mathematician Stefan Schwabik who died i... more This is the paper written in memory of outstanding Czech mathematician Stefan Schwabik who died in 2009.

Communications in Applied …, 2011

ABSTRACT. The boundary value problem on the half-line for the second order differential equation ... more ABSTRACT. The boundary value problem on the half-line for the second order differential equation with general Φ-Laplacian (a (t) Φ (x′))′= b (t) F (x), t≥ 0, x (0)= c> 0, 0< lim t→∞ x (t)<∞, x (t)> 0, lim t→∞ x′(t)= 0, is considered, where a, b are continuous functions on [ ...

Mathematica Bohemica, 2011

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Mathematica Bohemica, 2011

Applied Mathematics Letters, 2016

We establish some new criteria for the oscillation and asymptotic behaviour of solutions of the t... more We establish some new criteria for the oscillation and asymptotic behaviour of solutions of the third-order nonlinear neutral differential equation 1 p(t) 1 r(t) x(t) + a(t)x γ(t) + q(t)f x δ(t) = 0. Applications illustrating the results are given.

Archivum Mathematicum, 1980

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Tento CD-ROM je učebním textem nového typu využívající možností současné výpočetní techniky. Jde ... more Tento CD-ROM je učebním textem nového typu využívající možností současné výpočetní techniky. Jde o moderní způsob výuky matematické analýzy, kdy prostřednictvím počítačových technologií se student učí matematickou analýzu a naopak. Podnětem k vytvoření CD-ROMu byla potřeba zvýšit geometrickou představivost studentů a zmodernizovat výuku využitím moderních technologií.

The book you are holding contains scientific contributions of the participants of the internation... more The book you are holding contains scientific contributions of the participants of the international conference Colloquium on Differential Equations and Integration Theory, which was dedicated to the memory of our respected colleague Stefan Schwabik.

Applied Mathematics and Computation, 2014

In this article, a class of fourth-order difference equations with quasi-differences and a deviat... more In this article, a class of fourth-order difference equations with quasi-differences and a deviating argument is considered. We state new oscillation theorems for the super-linear and for the half-linear case and we complete the existing results in the literature.

Rocky Mountain Journal of Mathematics, 2010

Nonlinear Analysis: Theory, Methods & Applications, 1997

Nonlinear Analysis: Theory, Methods & Applications, 2008

In this paper, we investigate oscillation and asymptotic properties for three-dimensional systems... more In this paper, we investigate oscillation and asymptotic properties for three-dimensional systems of dynamic equations.

Journal of Mathematical Analysis and Applications, 1997

We continue the study of limit-pointrlimit-circle type differential equations of the nth order. I... more We continue the study of limit-pointrlimit-circle type differential equations of the nth order. In particular, we show that the differential expression y Ž4 k. q ry, k s 1, 2,. .. , is never of the limit-circle type as long as r is not an unbounded oscillatory function; this partially answers an open question and generalizes our result for n s 4. This follows as a consequence of new results on the nonlinear limit-pointrlimit-circle problem for the equation

Computers & Mathematics with Applications, 2004

The third-order nonlinear difference equations a(p~A(~.A~.)) + q.f(~+p) = 0, p e {0,1, 2}, where ... more The third-order nonlinear difference equations a(p~A(~.A~.)) + q.f(~+p) = 0, p e {0,1, 2}, where (p,~), (rn), and (qn) are sequences of positive real numbers for n E N, f : R-* ~ is a continuous function such that f(u)u > 0 for u =fi 0, are investigated. All nonoscillatory solutions of these equations are classified according to the sign of their quasiditterences to classes Ni, i = 0, 1, 2, 3, and sufficient conditions ensuring N~-0, i E {1, 2, 3} are given. Special attention is paid to equation (El) for which the generalized zeros of solutions are studied and an energy function F is introduced. The relation between the class No and solutions for which Fn < 0 for n E N is established. (~ 2004 Elsevier Ltd. All rights reserved.

Applicable Analysis, 1996

ABSTRACT

Journal of Mathematical Analysis and Applications, 2006

Necessary and sufficient conditions for the existence of at least one oscillatory solution of a s... more Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second-order quasilinear differential equation are presented. These results yield also new conditions guaranteeing the coexistence of oscillatory and nonoscillatory solutions. Our approach is based on the asymptotic representation of solutions by means of a periodic function and of a suitable zerocounting function.

Journal of Mathematical Analysis and Applications, 2006

Necessary and sufficient conditions for the existence of at least one oscillatory solution of a s... more Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second-order quasilinear differential equation are presented. These results yield also new conditions guaranteeing the coexistence of oscillatory and nonoscillatory solutions. Our approach is based on the asymptotic representation of solutions by means of a periodic function and of a suitable zerocounting function.

This is the paper written in memory of outstanding Czech mathematician Stefan Schwabik who died i... more This is the paper written in memory of outstanding Czech mathematician Stefan Schwabik who died in 2009.

Communications in Applied …, 2011

ABSTRACT. The boundary value problem on the half-line for the second order differential equation ... more ABSTRACT. The boundary value problem on the half-line for the second order differential equation with general Φ-Laplacian (a (t) Φ (x′))′= b (t) F (x), t≥ 0, x (0)= c> 0, 0< lim t→∞ x (t)<∞, x (t)> 0, lim t→∞ x′(t)= 0, is considered, where a, b are continuous functions on [ ...

Mathematica Bohemica, 2011

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Mathematica Bohemica, 2011

Applied Mathematics Letters, 2016

We establish some new criteria for the oscillation and asymptotic behaviour of solutions of the t... more We establish some new criteria for the oscillation and asymptotic behaviour of solutions of the third-order nonlinear neutral differential equation 1 p(t) 1 r(t) x(t) + a(t)x γ(t) + q(t)f x δ(t) = 0. Applications illustrating the results are given.

Archivum Mathematicum, 1980

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Tento CD-ROM je učebním textem nového typu využívající možností současné výpočetní techniky. Jde ... more Tento CD-ROM je učebním textem nového typu využívající možností současné výpočetní techniky. Jde o moderní způsob výuky matematické analýzy, kdy prostřednictvím počítačových technologií se student učí matematickou analýzu a naopak. Podnětem k vytvoření CD-ROMu byla potřeba zvýšit geometrickou představivost studentů a zmodernizovat výuku využitím moderních technologií.

The book you are holding contains scientific contributions of the participants of the internation... more The book you are holding contains scientific contributions of the participants of the international conference Colloquium on Differential Equations and Integration Theory, which was dedicated to the memory of our respected colleague Stefan Schwabik.

Applied Mathematics and Computation, 2014

In this article, a class of fourth-order difference equations with quasi-differences and a deviat... more In this article, a class of fourth-order difference equations with quasi-differences and a deviating argument is considered. We state new oscillation theorems for the super-linear and for the half-linear case and we complete the existing results in the literature.

Rocky Mountain Journal of Mathematics, 2010

Nonlinear Analysis: Theory, Methods & Applications, 1997

Nonlinear Analysis: Theory, Methods & Applications, 2008

In this paper, we investigate oscillation and asymptotic properties for three-dimensional systems... more In this paper, we investigate oscillation and asymptotic properties for three-dimensional systems of dynamic equations.

Journal of Mathematical Analysis and Applications, 1997

We continue the study of limit-pointrlimit-circle type differential equations of the nth order. I... more We continue the study of limit-pointrlimit-circle type differential equations of the nth order. In particular, we show that the differential expression y Ž4 k. q ry, k s 1, 2,. .. , is never of the limit-circle type as long as r is not an unbounded oscillatory function; this partially answers an open question and generalizes our result for n s 4. This follows as a consequence of new results on the nonlinear limit-pointrlimit-circle problem for the equation

Computers & Mathematics with Applications, 2004

The third-order nonlinear difference equations a(p~A(~.A~.)) + q.f(~+p) = 0, p e {0,1, 2}, where ... more The third-order nonlinear difference equations a(p~A(~.A~.)) + q.f(~+p) = 0, p e {0,1, 2}, where (p,~), (rn), and (qn) are sequences of positive real numbers for n E N, f : R-* ~ is a continuous function such that f(u)u > 0 for u =fi 0, are investigated. All nonoscillatory solutions of these equations are classified according to the sign of their quasiditterences to classes Ni, i = 0, 1, 2, 3, and sufficient conditions ensuring N~-0, i E {1, 2, 3} are given. Special attention is paid to equation (El) for which the generalized zeros of solutions are studied and an energy function F is introduced. The relation between the class No and solutions for which Fn < 0 for n E N is established. (~ 2004 Elsevier Ltd. All rights reserved.

Applicable Analysis, 1996

ABSTRACT

Journal of Mathematical Analysis and Applications, 2006

Necessary and sufficient conditions for the existence of at least one oscillatory solution of a s... more Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second-order quasilinear differential equation are presented. These results yield also new conditions guaranteeing the coexistence of oscillatory and nonoscillatory solutions. Our approach is based on the asymptotic representation of solutions by means of a periodic function and of a suitable zerocounting function.

Journal of Mathematical Analysis and Applications, 2006

Necessary and sufficient conditions for the existence of at least one oscillatory solution of a s... more Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second-order quasilinear differential equation are presented. These results yield also new conditions guaranteeing the coexistence of oscillatory and nonoscillatory solutions. Our approach is based on the asymptotic representation of solutions by means of a periodic function and of a suitable zerocounting function.