An existence result for a class of (p(x),q(x))-Laplacian system via sub-supersolution method
Saleh
Shakeri
Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, P. O. Box 678, Iran
author
text
article
2021
eng
This study concerns the existence of positive solution for the following nonlinear boundary value problem\begin{gather*}-\Delta_{p(x)} u= a(x)h(u) + f(v) \quad\text{in }\Omega\\-\Delta_{q(x)} v=b(x)k(v) + g(u) \quad\text{in }\Omega\\u=v= 0 \quad\text{on } \partial \Omega\end{gather*}where $p(x),q(x) \in C^1(\mathbb{R}^N)$ are radial symmetric functions such that $\sup|\nabla p(x)| < \infty,$ $\sup|\nabla q(x)|<\infty$ and $1 < \inf p(x) \leq \sup p(x) <\infty,1 < \inf q(x) \leq \sup q(x) < \infty$, and where $-\Delta_{p(x)} u = -\mathop{\rm div}|\nabla u|^{p(x)-2}\nabla u,-\Delta_{q(x)} v =-\mathop{\rm div}|\nabla v|^{q(x)-2}\nabla v$ respectively are called $p(x)$-Laplacian and $q(x)$-Laplacian, $\Omega = B(0 , R) = \{x | |x| < R\}$ is a bounded radial symmetric domain, where $R > 0$ is a sufficiently large constant. We discuss the existence of positive solution via sub-supersolutions without assuming sign conditions on $f(0)$ and $g(0)$.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
3
v.
4
no.
2021
1
8
http://www.macajournal.com/article_685401_bf81051cb14c0238acbe5412b52fd812.pdf
dx.doi.org/10.30495/maca.2021.1937515.1024
On closedness of convolution of two sets
Seyyed Mohammad
Tabatabaie
Department of Mathematics, University of Qom, Qom, Iran
author
text
article
2021
eng
In this note, we give an abstract version of the fact that convolution of two closed and compact subsets of a hypergroup is a closed set.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
3
v.
4
no.
2021
9
12
http://www.macajournal.com/article_685578_0667a5097e65cd0dc09860c42fe2a77f.pdf
dx.doi.org/10.30495/maca.2021.1935853.1020
On a nonlinear abstract second-order integrodifferential equation part I
Mohammed
Hussain
H.no 3-8-44\slash2(1-25-176), Manzoorpura, Near Shahgunj, Aurangabad (431001), Maharashtra, India
author
text
article
2021
eng
The object of this paper is to study the existence, uniqueness and continuation of the solutions of nonlinear second-order integrodifferential equations. In the theory of infinitesimal generator of $C_0$- semigroup in a Banach space, the fixed point theorems of Schauder and Banach are used to establish our main results.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
3
v.
4
no.
2021
13
24
http://www.macajournal.com/article_685579_252fa30ee6eae90f5a07fdad068b1c66.pdf
dx.doi.org/10.30495/maca.2021.1936023.1022
Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials
Mohammad Hossein
Derakhshan
Department of Industrial Engineering, Apadana Institute of Higher Education, Shiraz, Iran
author
text
article
2021
eng
In this paper, an efficient numerical method based on operational matrices of the second kind Chebyshev polynomials is used for the solution of a coupled system of fractional-order integrodifferential equations that the fractional derivative is given in Caputo's sense. The operational matrices of the second kind Chebyshev polynomials reduce the given equations to a system of linear algebraic equations. An approximate solution is calculated by extending the functions in terms of the second kind Chebyshev polynomials and applying operational matrices. Unknown coefficients are obtained by solving the final system of linear equations. Also, convergence analysis and error bound of the solution are studied in this paper. Moreover, to check the reliability and accuracy of the given method. The numerical examples have been shown and the results of the described method are compared with the Haar wavelet method. The obtained results authenticate that the displayed method is effortless to analyze and perform such types of problems. All methods for the proposed method are applied in MATLAB (R2020b) software.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
3
v.
4
no.
2021
25
40
http://www.macajournal.com/article_685644_23f14b286fa615fb690c448b625b9a9b.pdf
dx.doi.org/10.30495/maca.2021.1938222.1025
Multiplicity results for the nonlinear p-Laplacian fractional boundary value problems
Tawanda Gallan
Chakuvinga
Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey
author
Fatma Serap
Topal
Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey
author
text
article
2021
eng
This paper investigates the existence of single and multiple positive positive solutions of fractional differential equations with p-Laplacian by means of the Green's function properties, the Guo-Krasnosel'skii fixed point theorem, the monotone iterative technique accompanied by established sufficient conditions and the Leggett-Williams fixed point theorem. Additionally, the main results are illustrated by some examples to show their validity.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
3
v.
4
no.
2021
41
62
http://www.macajournal.com/article_686168_4d65d67d764c3138e2e501d1fba96748.pdf
dx.doi.org/10.30495/maca.2021.1938349.1026
Bifuzzy d-algebras under norms
Rasul
Rasuli
Department of Mathematics, Payame Noor University, Tehran, Iran.
author
text
article
2021
eng
In this paper, by using norms (t-norms and t-conorms), we introduce the notions of bifuzzy d-algebras and bifuzzy d-ideals of d-algebras and investigate several interesting properties. Next, we consider their intersection and product. Finally, we obtain some results about them under d-algebra homomorphisms.
Mathematical Analysis and its Contemporary Applications
A.I.A University Publishing Group.
2716-9890
3
v.
4
no.
2021
63
83
http://www.macajournal.com/article_685803_34880c5e15307e9ddc2ffe920f7829e7.pdf
dx.doi.org/10.30495/maca.2021.1938454.1027