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On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays

Beata Sikora (2019)

Kybernetika

The paper presents finite-dimensional dynamical control systems described by semilinear fractional-order state equations with multiple delays in the control and nonlinear function f . The relative controllability of the presented semilinear system is discussed. Rothe’s fixed point theorem is applied to study the controllability of the fractional-order semilinear system. A control that steers the semilinear system from an initial complete state to a final state at time t > 0 is presented. A numerical...

On BVPs in l∞(A).

Gerd Herzog, Roland Lemmert (2005)

Extracta Mathematicae

We prove the existence of extremal solutions of Dirichlet boundary value problems for u''a + fa(t,u,u'a) = 0 in l∞(A) between a generalized pair of upper and lower functions with respect to the coordinatewise ordering, and for f quasimonotone increasing in its second variable.

On discontinuous implicit differential equations in ordered Banach spaces with discontinuous implicit boundary conditions

S. Carl, S. Heikkilä (1999)

Annales Polonici Mathematici

We consider the existence of extremal solutions to second order discontinuous implicit ordinary differential equations with discontinuous implicit boundary conditions in ordered Banach spaces. We also study the dependence of these solutions on the data, and cases when the extremal solutions are obtained as limits of successive approximations. Examples are given to demonstrate the applicability of the method developed in this paper.

On existence theorems for semilinear equations and applications

Fang Zhang, Feng Wang (2013)

Annales Polonici Mathematici

Existence results for semilinear operator equations without the assumption of normal cones are obtained by the properties of a fixed point index for A-proper semilinear operators established by Cremins. As an application, the existence of positive solutions for a second order m-point boundary value problem at resonance is considered.

On fourth-order boundary-value problems

Myelkebir Aitalioubrahim (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We show the existence of solutions to a boundary-value problem for fourth-order differential inclusions in a Banach space, under Lipschitz’s contractive conditions, Carathéodory conditions and lower semicontinuity conditions.

On Ishlinskij's model for non-perfectly elastic bodies

Pavel Krejčí (1988)

Aplikace matematiky

The main goal of the paper is to formulate some new properties of the Ishlinskii hysteresis operator F , which characterizes e.g. the relation between the deformation and the stress in a non-perfectly elastic (elastico-plastic) material. We introduce two energy functionals and derive the energy inequalities. As an example we investigate the equation u ' ' + F ( u ) = 0 describing the motion of a mass point at the extremity of an elastico-plastic spring.

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