scholarly journals On a class of infinite system of third-order differential equations in lp via measure of noncompactness

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3861-3870
Author(s):  
E. Pourhadi ◽  
M. Mursaleen ◽  
R. Saadati
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Third Order ◽  
Banach Sequence Space ◽  
Existence Of Periodic Solutions ◽  
Banach Sequence

In this paper, with the help of measure of noncompactness together with Darbo-type fixed point theorem, we focus on the infinite system of third-order differential equations u???i + au??i + bu?i + cui = fi(t, u1(t), u2(t),...) where fi ? C(R x R?,R) is ?-periodic with respect to the first coordinate and a,b,c ? R are constants. The aim of this paper is to obtain the results with respect to the existence of ?-periodic solutions of the aforementioned system in the Banach sequence space lp (1 ? p < ?) utilizing the respective Green?s function. Furthermore, some examples are provided to support our main results.

scholarly journals Multiplicity of Periodic Solutions for Third-Order Nonlinear Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Xuxin Yang ◽  
Weibing Wang ◽  
Dingyang Lv
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Operator ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Integrodifferential Equation ◽  
Nonlinear Differential Equations ◽  
Third Order ◽  
Existence Of Periodic Solutions ◽  
Linear Integral

We study the existence of periodic solutions for third-order nonlinear differential equations. The method of proof relies on Schauder’s fixed point theorem applied in a novel way, where the original equation is transformed into second-order integrodifferential equation through a linear integral operator. Finally, examples are presented to illustrate applications of the main results.

scholarly journals Solvability for infinite systems of fractional differential equations in Banach sequence spaces lp and c0

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 3943-3955
Author(s):  
Ayub Samadi ◽  
Sotiris Ntouyas
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Existence Results ◽  
Infinite Systems ◽  
Banach Sequence Spaces ◽  
Fractional Differential ◽  
Banach Sequence

This paper is devoted to an infinite system of nonlinear fractional differential equations in the Banach spaces c0 and lp with p ? 1. Existence results are obtained, by using the theory of measure of noncompactness and a new generalization of Darbo?s fixed point theorem. Some examples are also included to show the efficiency of our results.

Weak Solutions for Fractional Differential Equations via Henstock–Kurzweil–Pettis Integrals

2020 ◽  
Vol 21 (2) ◽  
pp. 135-145 ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Measure Of Noncompactness ◽  
Pettis Integral ◽  
Existence Of Weak Solutions ◽  
Fractional Differential

AbstractIn this paper, we used Henstock–Kurzweil–Pettis integral instead of classical integrals. Using fixed point theorem and weak measure of noncompactness, we study the existence of weak solutions of boundary value problem for fractional integro-differential equations in Banach spaces. Our results generalize some known results. Finally, an example is given to demonstrate the feasibility of our conclusions.

scholarly journals Existence solution of a system of differential equations using generalized Darbo's fixed point theorem

2021 ◽  
Vol 6 (12) ◽  
pp. 13358-13369
Author(s):  
Rahul ◽  
◽  
Nihar Kumar Mahato
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solution ◽  
System Of Differential Equations ◽  
Darbo’S Fixed Point Theorem ◽  
Darbo Fixed Point Theorem

<abstract><p>In this paper, we proposed a generalized of Darbo's fixed point theorem via the concept of operators $ S(\bullet; .) $ associated with the measure of noncompactness. Using this generalized Darbo fixed point theorem, we have given the existence of solution of a system of differential equations. At the end, we have given an example which supports our findings.</p></abstract>

scholarly journals Applications of measures of noncompactness to infinite system of fractional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3421-3432 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Bilal Bilalov ◽  
Syed Rizvi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Result ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Hausdorff Measure Of Noncompactness ◽  
Measures Of Noncompactness ◽  
Banach Sequence Spaces ◽  
Fractional Differential ◽  
Banach Sequence

In this paper, we discuss few existence result for solution of an infinite system of fractional differential equations of order ?(1 < ? < 2), with three point boundary value problem in the interval [0, T]. The problem is studied in the classical Banach sequence spaces c0 and lp (1 ? p < 1), using Hausdorff measure of noncompactness and Darbo type fixed point theorem. We also illustrate our results through some concrete examples.

Application of Measure of Noncompactness to Infinite Systems of Differential Equations

2013 ◽  
Vol 56 (2) ◽  
pp. 388-394 ◽  
Author(s):  
M. Mursaleen
Keyword(s):  
Differential Equations ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Sequence Spaces ◽  
Measures Of Noncompactness ◽  
Infinite Systems ◽  
Systems Of Differential Equations ◽  
Banach Sequence Spaces ◽  
Banach Sequence

AbstractIn this paper we determine theHausdorff measure of noncompactness on the sequence space n(ϕ) ofW. L. C. Sargent. Further we apply the technique of measures of noncompactness to the theory of infinite systems of differential equations in the Banach sequence spaces n(ϕ) and m(ϕ). Our aim is to present some existence results for infinite systems of differential equations formulated with the help of measures of noncompactness.

scholarly journals Solvability of an infinite system of nonlinear integral equations of Volterra-Hammerstein type

2019 ◽  
Vol 9 (1) ◽  
pp. 1187-1204
Author(s):  
Agnieszka Chlebowicz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Function Space ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Half Axis ◽  
Suitable Measure

Abstract The purpose of the paper is to study the solvability of an infinite system of integral equations of Volterra-Hammerstein type on an unbounded interval. We show that such a system of integral equations has at least one solution in the space of functions defined, continuous and bounded on the real half-axis with values in the space l1 consisting of all real sequences whose series is absolutely convergent. To prove this result we construct a suitable measure of noncompactness in the mentioned function space and we use that measure together with a fixed point theorem of Darbo type.

scholarly journals Existence of solutions of nonlinear differential equations with deviating arguments

1991 ◽  
Vol 44 (3) ◽  
pp. 467-476
Author(s):  
K. Balachandran ◽  
S. Ilamaran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We prove an existence theorem for nonlinear differential equations with deviating arguments and with implicit derivatives. The proof is based on the notion of measure of noncompactness and the Darbo fixed point theorem.

scholarly journals An existence theorem for nonlinear delay differential equations

1989 ◽  
Vol 2 (2) ◽  
pp. 85-89
Author(s):  
Krishnan Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Delay Differential Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

In this paper we prove a theorem on the existence of solutions of nonlinear delay differential equations, with implicit derivatives. The result is established using the measure of noncompactness of a set and Darbo's fixed point theorem.

scholarly journals Positive solutions of infinite coupled system of fractional differential equations in the sequence space of weighted means

2021 ◽  
Vol 7 (2) ◽  
pp. 2680-2694
Author(s):  
Majid Ghasemi ◽  
◽  
Mahnaz Khanehgir ◽  
Reza Allahyari ◽  
Hojjatollah Amiri Kayvanloo
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Real Numbers ◽  
Weighted Means ◽  
Fractional Differential

<abstract><p>We first discuss the existence of solutions of the infinite system of $ (n-1, n) $-type semipositone boundary value problems (BVPs) of nonlinear fractional differential equations</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} D^{\alpha}_{0_+}u_i(\rho)+\eta f_i(\rho,v(\rho)) = 0,&amp; \rho\in(0,1), \\ D^{\alpha}_{0_+}v_i(\rho)+\eta g_i(\rho,u(\rho)) = 0,&amp; \rho\in(0,1), \\u_i^{(j)}(0) = v_{i}^{(j)}(0) = 0,&amp; 0\leq j\leq n-2, \\ u_{i}(1) = \zeta\int_0^1 u_i(\vartheta)d\vartheta, \ v_{i}(1) = \zeta\int_0^1 v_i(\vartheta)d\vartheta,&amp; i\in\mathbb{N},\\ \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>in the sequence space of weighted means $ c_0(W_1, W_2, \Delta) $, where $ n\geq3 $, $ \alpha\in(n-1, n] $, $ \eta, \zeta $ are real numbers, $ 0 &lt; \eta &lt; \alpha, $ $ D^{\alpha}_{0_+} $ is the Riemann-Liouville's fractional derivative, and $ f_i, g_i, $ $ i = 1, 2, \ldots $, are semipositone and continuous. Our approach to the study of solvability is to use the technique of measure of noncompactness. Then, we find an interval of $ \eta $ such that for each $ \eta $ lying in this interval, the system of $ (n-1, n) $-type semipositone BVPs has a positive solution. Eventually, we demonstrate an example to show the effectiveness and usefulness of the obtained result.</p></abstract>

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