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1
Content available Concavity of solutions of a 2n-th order problem with symmetry
Twaty A. A., Eloe P. W.
Opuscula Mathematica
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2013
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Vol. 33, no. 4
603--613
EN
In this article we apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a 2n-th order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach space. Inequalities that extend the notion of concavity to 2n-th order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.
2
Content available remote Juliusz Schauder, topology of function spaces and Partial Differential Equations
Mawhin J.
Wiadomości Matematyczne
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2012
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T. 48, Nr 2
173--183
3
Content available Boundary value problems for n-th order differential inclusions with four-point integral boundary conditions
Ahmad B., Ntouyas S. K.
Opuscula Mathematica
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2012
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Vol. 32, no. 2
205-226
EN
In this paper, we discuss the existence of solutions for a four-point integral boundary value problem of n-th order differential inclusions involving convex and non-convex multivalued maps. The existence results are obtained by applying the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.
4
Content available remote Initial value problems for second-order integro-differential equations on unbounded domains in Banach space
Liu Y.
Demonstratio Mathematica
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2005
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Vol. 38, nr 2
349--364
EN
In this paper, the Monch fixed point theorem is used to investigate the existence of solutions of initial value problem (IVP, for short) for second order nonlinear integro-differential equations on infinite intervals in a Banach space. At the same time, the uniqueness of solution for IVP is obtained also.
5
Content available remote Application of a theorem of Earle and Hamilton to the theory of scattering and transport
Redheffer R.
Demonstratio Mathematica
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2005
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Vol. 38, nr 1
59--68
6
Content available remote Generalized I-nonexpansive maps and best approximations in Banach spaces
Shahzad N.
Demonstratio Mathematica
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2004
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Vol. 37, nr 3
597--600
EN
A noncommutative version of a best approximation result for generalized I-nonexpansive maps is obtained.
7
Content available remote Nonoscillatory solutions of delay difference equations with oscillating coefficients
Bolat Y., Akin Ö.
Demonstratio Mathematica
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2003
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Vol. 36, nr 4
859--866
EN
Our aim in this paper is to obtain sufficient conditions under which certain difference equations have a "large" number of non-oscillatory solutions. Using the characteristic equation of a "majorant" delay difference equation with oscillating coefficients and Schauder's fixed point theorem, we obtain conditions under which the difference equation in question has a non-oscillatory solution.
8
Content available remote A semilinear wave equation associated with a nonlinear integral equation
Long N. T., Thuyet T. M.
Demonstratio Mathematica
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2003
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Vol. 36, nr 4
915--938
9
Content available remote Detection and Control Problems for Non-Linear Distributed-Parameter Systems With Delays
Namir A., Lahmidi F., Labriji E. H.
International Journal of Applied Mathematics and Computer Science
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2000
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Vol. 10, no 3
437-464
EN
First, we consider non-linear discrete-time and continuous-time systems with unknown inputs. The problem of reconstructing an input using the information given by an output equation is investigated. Then we examine a control problem for non-linear discrete-time hereditary systems, i.e. the problem of finding a control which drives the state of the system from its initial value to a given desired final state. The methods used to solve these problems are based on the state-space technique and fixed-point theorems. To illustrate the outlined ideas, various numerical simulation results are presented.
10
Content available Schauder's fixed-point theorem in nonlinear controllability problems
Klamka J.
Control and Cybernetics
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2000
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Vol. 29, no 1
153-165
EN
This paper refers to application of the Schauder's fixed point theorem together with linear controllability results in getting the sufficient controllability conditions for various kinds of controllability and for different types of nonlinear control systems. The following nonlinear control systems are considered : finite-dimensional systems, systems with delays in control or in the state variables, and infinite-dimensional systems. The paper presents the review of results existing in the literature which show how Schauder's fixed-point theorem can be practically used to solve several controllability problems for different types of nonlinear control systems.
11
Content available remote A note on the abstract Cauchy-Kovalevskaya theorem
Ghisi M.
Demonstratio Mathematica
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1999
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Vol. 32, nr 2
331-343
EN
We give a version of the abstract Cauchy-Kovalevskaya Theorem for the Cauchy problem u'= A(t, u), u(O)=u0 when A is not necessarily a Lipschitz continuous operator. The operator A(t,u)= F(t,u,u) verifies 1) F:1 I x Br1,R x Br,R- X3 for s < r < ro (r1 < ro is fixed), F(t, u, .) is Lipschitz continuous, and F(t, ., ,) is alpha-Lipshitz continuous or 2 ) F : I x Br1 , R x X r - X 9 for s< r < ro (r1 < ro is fixed), and F(t, ., .) is alpha-Lipschitz continuous , where Br,R denotes the ball of radius R in Xr. We prove the result by using Tonelli approximations and fixed point theorems.
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