On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications

Some Nonlinear Weakly Singular Integral Inequalities with Two Variables and Applications

Various singular integral inequalities play an important role in the development of the theory of differential equations, functional differential equations, and integral equations. For example, Henry 1 proposed a linear integral inequality with singular kernel to investigate some qualitative properties for a parabolic differential equation, and Sano and Kunimatsu 2 gave a modified version of He...

Some New Nonlinear Weakly Singular Integral Inequalities of Wendroff Type with Applications

the study of bright and surface discrete cavity solitons dynamics in saturable nonlinear media

امروزه سالیتون ها بعنوان امواج جایگزیده ای که تحت شرایط خاص بدون تغییر شکل در محیط منتشر می-شوند، زمینه مطالعات گسترده ای در حوزه اپتیک غیرخطی هستند. در این راستا توجه به پدیده پراش گسسته، که بعنوان عامل پهن شدگی باریکه نوری در آرایه ای از موجبرهای جفت شده، ظاهر می گردد، ضروری است، زیرا سالیتون های گسسته از خنثی شدن پراش گسسته در این سیستم ها بوسیله عوامل غیرخطی بوجود می آیند. گسستگی سیستم عامل...

On some new weakly singular Volterra integral inequalities with maxima and their applications

*Correspondence: [email protected] Department of Mathematics, Sichuan University for Nationalities, Kangding, Sichuan 626001, P.R. China Abstract In this paper, we consider a general form of nonlinear integral inequalities with the unknown function composed with a given function on the left hand side, more than one distinct nonlinear integrals on its right-hand side, and weakly singular kernels,...

Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also ...