Browsing by Subject "fixed point"

Now showing 1 - 12 of 12

Access status: Open Access ,
Controllability of semilinear systems with fixed delay in control
(2015) Kumar, Surendra; Sukavanam, N.
In this paper, different sufficient conditions for exact controllability of semilinear systems with a single constant point delay in control are established in infinite dimensional space. The existence and uniqueness of mild solution is also proved under suitable assumptions. In particular, local Lipschitz continuity of a nonlinear function is used. To illustrate the developed theory some examples are given.
Access status: Open Access ,
Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay
(2014) Arjunan, M. Mallika; Nadaf, N. Y.
In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii’s fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.
Access status: Open Access ,
Existence of periodic solutions for totally nonlinear neutral differential equations with functional delay
(2012) Yankson, Ernest
We use a variant of Krasnoselskii’s fixed point theorem by T.A. Burton to show that the nonlinear neutral differential equation with functional delay $x'(t) = -a(t)h(x(t)) +c(t)x'(t-g(t)) + q(t,x(t) x(t-g(t)))$ has a periodic solution.
Access status: Open Access ,
Fixed point theorems for a semigroup of total asymptotically nonexpansive mappings in uniformly convex Banach spaces
(2014) Suantai, Suthep; Phuengrattana, Withun
In this paper, we provide existence and convergence theorems of common fixed points for left (or right) reversible semitopological semigroups of total asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results announced by other authors.
Access status: Open Access ,
Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple delay
(2013) Abbas, Saïd; Benchohra, Mouffak
In the present paper we investigate the existence of solutions for a system of integral inclusions of fractional order with multiple delay. Our results are obtained upon suitable fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler for the nonconvex case.
Access status: Open Access ,
More on the behaviors of fixed points sets of multifunctions and applications
(2015) Alleche, Boualem; Nachi, Khadra
In this paper, we study the behaviors of fixed points sets of non necessarily pseudo-contractive multifunctions. Rather than comparing the images of the involved multifunctions, we make use of some conditions on the fixed points sets to establish general results on their stability and continuous dependence. We illustrate our results by applications to differential inclusions and give stability results of fixed points sets of non necessarily pseudo-contractive multifunctions with respect to the bounded proximal convergence.
Access status: Open Access ,
On a nonlinear integrodifferential evolution inclusion with nonlocal initial conditions in Banach spaces
(2012) Yan, Zuomao
In this paper, we discuss the existence results for a class of nonlinear integrodifferential evolution inclusions with nonlocal initial conditions in Banach spaces. Our results are based on a fixed point theorem for condensing maps due to Martelli and the resolvent operators combined with approximation techniques.
Access status: Open Access ,
Positive solutions of a singular fractional boundary value problem with a fractional boundary condition
(2017) Lyons, Jeffrey W.; Neugebauer, Jeffrey T.
For $\alpha\in(1,2]$ the singular fractional boundary value problem $D^{\alpha}_{0^+}x+f\left(t,x,D^{\mu}_{0^+}x\right)=0,\quad 0\lt t\lt 1,$ satisfying the boundary conditions $x(0)=D^{\beta}_{0^+}x(1)=0$, where $\beta\in(0,\alpha-1]$, $\mu\in(0,\alpha-1]$, and $D^{\alpha}_{0^+}$, $D^{\beta}_{0^+}$ and $D^{\mu}_{0^+}$ are Riemann-Liouville derivatives of order $\alpha$, $\beta$, and $\mu$ respectively, is considered. Here $f$ satisfies a local Carathéodory condition, and $f(t, x, y)$ may be singular at the value 0 in its space variable $x$. Using regularization and sequential techniques and Krasnosel’skii’s fixed point theorem, it is shown this boundary value problem has a positive solution. An example is given.
Access status: Open Access ,
Singular quasilinear convective systems involving variable exponents
(Wydawnictwa AGH, 2024) Moussaoui, Abdelkrim; Nabab, Dany; Vélin, Jean
The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. The approach combines the sub-supersolutions method and Schauder's fixed point theorem.
Access status: Open Access ,
Solutions of fractional nabla difference equations - existence and uniqueness
(2016) Jonnalagadda, Jagan Mohan
In this article, we discuss existence, uniqueness and dependency of solutions of nonlinear fractional nabla difference equations in a Banach space equipped with a suitable norm, using the contractive mapping approach. As an application of the established results we present and analyse a few examples.
Access status: Open Access ,
Stability by Krasnoselskii's theorem in totally nonlinear neutral differential equations
(2013) Derrardjia, Ishak; Ardjouni, Abdelouaheb; Djoudi, Ahcene
In this paper we use fixed point methods to prove asymptotic stability results of the zero solution of a class of totally nonlinear neutral differential equations with functional delay. The study concerns $x'(t)=a(t)x^3(t)+c(t)x'(t-r(t))+b(t)x^3(t-r(t)).$ The equation has proved very challenging in the theory of Liapunov's direct method. The stability results are obtained by means of Krasnoselskii-Burton's theorem and they improve on the work of T.A. Burton (see Theorem 4 in [Liapunov functionals, fixed points, and stability by Krasnoselskii's theorem, Nonlinear Studies 9 (2001), 181-190]) in which he takes $c=0$ in the above equation.
Access status: Open Access ,
Surveys of creep-susceptible locations using the method of fixed points in jointless rail track
(2010) Strach, Michał; Kampczyk, Arkadiusz
The article deals with the problems as well as principles of conducting surveys and observations of creep-susceptible locations of rail courses in a jointless rail track using the method of fixed points. The paper presents and discusses the results of authors- surveys of rail courses creep of the No. 1 jointless rail track of the railway line No. 161 Katowice-Szopienice Północne - Chorzów Stary, which were carried out in the spring of 2008 and 2009. The total length of the jointless rail track covered by the monitoring was 5.227 km. The distribution velocity at this section equaled to 80 km/h. In addition, photographs and own observations on the relevant issues were presented. Due to the limitations in size, the article sets out the most important aspects of conducting surveying works, which are to determine the occurring shifts as well as to mark the fixed points and reference points. It also presents the manner of carrying out the analysis and final assessment of the jointless rail track operation.