Browsing by Subject "fixed point theorem"

Now showing 1 - 7 of 7

Access status: Open Access ,
A class of nonlocal integrodifferential equations via fractional derivative and its mild solutions
(2011) Wang, JinRong; Yan, X.; Zhang, X.-H.; Wang, T.-M.; Li, X.-Z.
In this paper, we discuss a class of integrodifferential equations with nonlocal conditions via a fractional derivative of the type $\begin{aligned}D_{t}^{q}x(t)=Ax(t)+\int\limits_{0}^{t}B(t-s)x(s)ds+t^{n}f\left(t,x(t)\right),&\;t\in [0,T],\;n\in Z^{+},\\&q\in(0,1],\;x(0)=g(x)+x_{0}.\end{aligned}$ Some sufficient conditions for the existence of mild solutions for the above system are given. The main tools are the resolvent operators and fixed point theorems due to Banach's fixed point theorem, Krasnoselskii's fixed point theorem and Schaefer's fixed point theorem. At last, an example is given for demonstration.
Access status: Open Access ,
Boundary value problems for second order delay differential equations
(2012) Skóra, Lidia
We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order.
Access status: Open Access ,
Existence and attractivity results for nonlinear first order random differential equations
(2010) Dhage, Bapurao C.; Ntouyas, Sotiris K.
In this paper, the existence and attractivity results are proved for nonlinear first order ordinary random differential equations. Two examples are provided to demonstrate the realization of the abstract developed theory.
Access status: Open Access ,
Fractional nonlocal integrodifferential equations of mixed type with time-varying generating operators and optimal control
(Wydawnictwa AGH, 2010) Wang, JinRong; Wei, W.; Yang, YanLong
In this paper, a class of fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is considered. Using a contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequality, the existence and uniqueness of mild solution are given. The existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is also presented.
Access status: Restricted ,
Istnienie rozwiązań dodatnich dla pewnej klasy problemów brzegowych
(Data obrony: 2009-07-08) Goncerz, Paweł
Wydział Matematyki Stosowanej
Access status: Open Access ,
Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn
(Wydawnictwa AGH, 2022) Bachar, Imed; Mâagli, Habib; Eltayeb, Hassan
In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of $\mathbb{R}^n$ ($n \geq 2$). The global behavior of this solution is also given.
Access status: Open Access ,
Right focal boundary value problems for difference equations
(2010) Henderson, Johnny; Liu, Xueyan; Lyons, Jeffrey W.; Neugebauer, Jeffrey T.
An application is made of a new Avery et al. fixed point theorem of compression and expansion functional type in the spirit of the original fixed point work of Leggett and Williams, to obtain positive solutions of the second order right focal discrete boundary value problem. In the application of the fixed point theorem, neither the entire lower nor entire upper boundary is required to be mapped inward or outward. A nontrivial example is also provided.