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5 Demonstratio Mathematica

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Global existence for abstract nonlinear Volterra-Fredholm functional integrodifferential equation

Dhakne M. B., Kucche K. D.

Demonstratio Mathematica

2012

Vol. 45, nr 1

117-127

In the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra-Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray-Schauder alternative and rely on a priori bounds of solution.

On the existence of global solutions of evolution equations

Medved M.

Demonstratio Mathematica

2004

Vol. 37, nr 4

871--882

In this paper a sufficient condition for the existence of global solutions of evolution equations is proved. In the proof a modification of the Bihari type integral inequality to the case of a weakly singular nonlinear integral inequality is used. An application to a reaction-diffusion problem is given.

On existence and stability of forced periodic oscillations for a rod in the viscous fluid

Hajdukiewicz M.

Demonstratio Mathematica

2004

Vol. 37, nr 1

91--100

The paper is devoted to the development of a numerical algorithm for finding the time-periodic transverse oscillations of a rod under external forces. Moreover, the dynamical stablility of these oscillations is proved under damping properities of the fluid.

Qualitative behaviour of an integral equation related to some epidemic model

Brestovanská E.

Demonstratio Mathematica

2003

Vol. 36, nr 3

603--609

Sufficient conditions for the uniqueness, global existence and for the convergence to zero when t -> oo of solutions of an integral equation related to an epidemic model are proved. The existence result is proved by applying the Banach fixed point theorem and for the proof of the convergence result a new type of integral inequality is used.

Asymptotics of pseudodifferential parabolic equations

Cholewa J. W., Dłotko T., Turski A. W.

Demonstratio Mathematica

2002

Vol. 35, nr 1

74-91

The paper provides new type examples covered by the general theory of global attractors for abstract parabolic equations presented in the monograph [C-D 1]. Inside the class of sectorial equations of the form (1) u+Au = F(u), t > 0, u(0) = uo, we cover pseudodifferential parabolic problems (2) m = -(-A)u + f(u), a należy (0,1), studied with suitable initial-boundary conditions and also their generalizations to problems with the main part being a finite sum of the fractional powers.