Browsing by Subject "existence"

Now showing 1 - 20 of 20

Access status: Open Access ,
Boundary value problems for n-th order differential inclusions with four-point integral boundary conditions
(2012) Bashir, Ahmad Khuda Bakhsh; Ntouyas, Sotiris K.
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.
Access status: Open Access ,
Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions
(2013) Ntouyas, Sotiris K.
This paper studies the boundary value problem of nonlinear fractional differential equations and inclusions of order $q \in (1,2]$ with nonlocal and integral boundary conditions. Some new existence and uniqueness results are obtained by using fixed point theorems.
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 stabilizability of steady-state for semilinear pulse-width sampler controlled system
(2011) Wang, JinRong
In this paper, we study the steady-state of a semilinear pulse-width sampler controlled system on infinite dimensional spaces. Firstly, by virtue of Schauder's fixed point theorem, the existence of periodic solutions is given. Secondly, utilizing a generalized Gronwall inequality given by us and the Banach fixed point theorem, the existence and stabilizability of a steady-state for the semilinear control system with pulse-width sampler is also obtained. At last, an example is given for demonstration.
Access status: Open Access ,
Existence and uniqueness results for fractional differential equations with boundary value condition
(2011) Lv, LinLi; Wang, JinRong; Wei, Wei
In this paper, we study the existence and uniqueness of fractional differential equations with boundary value conditions. A new generalized singular type Gronwall inequality is given to obtain important a priori bounds. Existence and uniqueness results of solutions are established by virtue of fractional calculus and fixed point method under some weak conditions. An example is given to illustrate the results.
Access status: Open Access ,
Existence of critical elliptic systems with boundary singularities
(2013) Yang, Jianfu; Zhou, Yimin
In this paper, we are concerned with the existence of positive solutions of the following nonlinear elliptic system involving critical Hardy-Sobolev exponent $\begin{equation*}\label{eq:1}(*) \left\{ \begin{array}{lll} -\Delta u= \frac{2\alpha}{\alpha+\beta}\frac{u^{\alpha-1}v^\beta}{|x|^s}-\lambda u^p, & \quad {\rm in}\quad \Omega,\\[2mm] -\Delta v= \frac{2\beta}{\alpha+\beta}\frac{u^\alpha v^{\beta-1}}{|x|^s}-\lambda v^p, & \quad {\rm in}\quad \Omega,\\[2mm] u\gt 0, v\gt 0, &\quad {\rm in}\quad \Omega,\\[2mm] u=v=0, &\quad {\rm on}\quad \partial\Omega, \end{array} \right. \end{equation*}$ where $N\geq 4$ and $\Omega$ is a $C^1$ bounded domain in $\mathbb{R}^N$ with $0\in\partial\Omega$. $0\lt s \lt 2$, $\alpha+\beta=2^*(s)=\frac{2(N-s)}{N-2}$, $\alpha,\beta\gt 1$, $\lambda\gt 0$ and $1 \lt p\lt \frac{N+2}{N-2}$. The case when 0 belongs to the boundary of $\Omega$ is closely related to the mean curvature at the origin on the boundary. We show in this paper that problem $(*)$ possesses at least a positive solution.
Access status: Open Access ,
Existence results for mild solutions of impulsive periodic systems
(2012) Yang, YanLong; Wang, JinRong
By applying the Horn’s fixed point theorem, we prove the existence of $T_0$-periodic $PC$-mild solution of impulsive periodic systems when $PC$-mild solutions are ultimate bounded.
Access status: Open Access ,
Existence results for random fractional differential equations
(2014) Lupulescu, Vasile; O'Regan, Donal; Rahman, Ghaus ur
In this paper, an existence result for a random fractional differential equation is established under a Carathéodory condition. Existence results for extremal random solutions are also proved. Finally, an existence and uniqueness result is given.
Access status: Open Access ,
Existence, uniqueness and estimates of classical solutions to some evolutionary system
(2015) Sapa, Lucjan
The theorem of the local existence, uniqueness and estimates of solutions in Hölder spaces for some nonlinear differential evolutionary system with initial conditions is formulated and proved. This system is composed of one partial hyperbolic second-order equation and an ordinary subsystem with a parameter. In the proof of the theorem we use the Banach fixed-point theorem, the Arzeli-Ascola lemma and the integral form of the differential problem.
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 i jednoznaczność rozwiązania klasycznego układu ewolucyjnych równań różniczkowych
(Data obrony: 2017-07-10) Światłowska, Julita
Wydział Matematyki Stosowanej
Access status: Restricted ,
Metoda prostych dla różniczkowo-funkcyjnych równań parabolicznych
(Data obrony: 2017-07-18) Kądziela, Agnieszka
Wydział Matematyki Stosowanej
Access status: Open Access ,
Multi-valued codensing random operators and functional random integral inclusions
(2011) Dhage, Bapurao C.
In this paper, some random fixed point theorems for continuous and condensing multi-valued random operators are proved and they are further applied to the random integral inclusions for proving the existence of the solutions via the priori bound method.
Access status: Open Access ,
On nonlocal problems for fractional differential equations in Banach spaces
(2011) Dong, XiWang; Wang, JinRong; Zhou, Yong
In this paper, we study the existence and uniqueness of solutions to the nonlocal problems for the fractional differential equation in Banach spaces. New sufficient conditions for the existence and uniqueness of solutions are established by means of fractional calculus and fixed point method under some suitable conditions. Two examples are given to illustrate the results.
Access status: Open Access ,
On some impulsive fractional differential equations in Banach spaces
(2010) Wang, JinRong; Wei, W.; Yang, YanLong
This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of $PC$-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration.
Access status: Open Access ,
Parabolic turbulence k-epsilon model with applications in fluid flows through permeable media
(Wydawnictwa AGH, 2024) Oliveira, Hermenegildo Borges de
In this work, we study a one-equation turbulence $k$-epsilon model that governs fluid flows through permeable media. The model problem under consideration here is derived from the incompressible Navier-Stokes equations by the application of a time-averaging operator used in the $k$-epsilon modeling and a volume-averaging operator that is characteristic of modeling unsteady porous media flows. For the associated initial- and boundary-value problem, we prove the existence of suitable weak solutions (average velocity field and turbulent kinetic energy) in the space dimensions of physics interest.
Access status: Open Access ,
Rafał Wojaczek's »Sickness Unto Non-Existence«
(Wydawnictwa AGH, 2018) Małecka, Anna
The paper focuses upon the philosophical message rendered by Rafał Wojaczek's poetry. The author regards the issue of non‑existence as the central theme of Wojaczek's creative output, and analyses it in the context of existentialist philosophy, referring to Martin Heidegger's concepts in particular. The following four aspects of the leading idea of non‑existence are identified and discussed in the article: non‑existence understood as death which not only constitutes everyone's destiny but also validates individual life, non‑existence as nothingness which is disclosed in anxiety, with the retreat of being in its entirety, non‑existence as a blurred personal identity, and, finally, non‑existence as a condition of creativity. The unique form and style of this poetry are considered to play an essential role in conveying the metaphysical content.
Access status: Open Access ,
Random integral equations on time scales
(2013) Lupulescu, Vasile; Lungan, Cristina
In this paper, we present the existence and uniqueness of random solution of a random integral equation of Volterra type on time scales. We also study the asymptotic properties of the unique random solution.
Access status: Open Access ,
Solutions for a nonhomogeneous p&q-Laplacian problem via variational methods and sub-supersolution technique
(Wydawnictwa AGH, 2023) Tavares, Leandro S.; Sousa, José Vanterler
In this paper it is obtained, through variational methods and sub-supersolution arguments, existence and multiplicity of solutions for a nonhomogeneous problem which arise in several branches of science such as chemical reactions, biophysics and plasma physics. Under a general hypothesis it is proved an existence result and multiple solutions are obtained by considering an additional natural condition.
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.