Journal of Mathematical Analysis and its Contemporary Applications
Volume:3 Issue: 4, Autumn 2021

This study concerns the existence of positive solution for the following nonlinear boundary value problem −∆p(x)u = a(x)h(u) + f(v) in Ω −∆q(x)v = b(x)k(v) + g(u) in Ω u = v = 0 on ∂Ω where p(x), q(x) ∈ C 1 (R N ) are radial symmetric functions such that sup |∇p(x)| < ∞, sup |∇q(x)| < ∞ and 1 < inf p(x) ≤ sup p(x) < ∞, 1 < inf q(x) ≤ sup q(x) < ∞, and where −∆p(x)u = − div |∇u| p(x)−2∇u, −∆q(x)v = − div |∇v| q(x)−2∇v respectively are called p(x)-Laplacian and q(x)-Laplacian, Ω = 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).

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.

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.

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.

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.

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.