Fractal and Fractional, 2023 The nonlinear Volterra–Fredholm integral Equation (NVFIE) with a singular kernel is discussed such that the kernel of position can take the Hilbert kernel form, Carleman function, logarithmic form, or Cauchy kernel. Using the quadrature method, the NVFIE
Sahar M. Abusalim +3 more
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Nonlinear integral equations singular in the dependent variable
Applied Mathematics Letters, 2007 This paper concerns the existence of nonnegative solutions to the singular integral equation \(y(t)=\int^1_0 k(t,s)[G(s,y(s))+F(s,y(s))]ds\) \((t\in [0,1])\), where \(G\in C([0,1]\times (0,\infty),[0,\infty))\), \(F\in C([0,1]\times [0,\infty),[0,\infty))\) so \(G\) may be singular at \(y=0\).
Kanishka Perera +2 more
exaly +4 more sources
Existence of solutions for a class of nonlinear Volterra singular integral equations
Computers and Mathematics With Applications, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Józef Banas +2 more
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Positive solutions of a boundary value problem with integral boundary conditions [PDF]
, 2011 We consider boundary-value problems studied in a recent paper. We show that some existing theory developed by Webb and Infante applies to this problem and we use the known theory to show how to find improved estimates on parameters μ*, λ so ...
Webb, J.
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Existence and uniqueness of solutions for a singular system of higher-order nonlinear fractional differential equations with integral boundary conditions [PDF]
Nonlinear Analysis, 2013 In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions.
Lin Wang, Xingqiu Zhang, Xinyi Lu
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Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks
Mathematics, 2022 A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems.
Ilya Boykov +2 more
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On Nonlinear Integral Inequalities of Gronwall Type in Two Variables [PDF]
, 2003 In this paper we obtain some new nonlinear integral inequality of Gronwall type involving functions of two independent variables which can be used in the analysis of the behavior of the solutions of some partial differential ...
Kim, Young-Ho, Dragomir, Sever S
core +6 more sources
Computation of semi-analytical solutions of fuzzy nonlinear integral equations
Advances in Difference Equations, 2020 In this article, we use a fuzzy number in its parametric form to solve a fuzzy nonlinear integral equation of the second kind in the crisp case. The main theme of this article is to find a semi-analytical solution of fuzzy nonlinear integral equations. A
Zia Ullah +3 more
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SINGULAR INTEGRAL EQUATIONS AND APPLICATIONS TO NONLINEAR CONJUGATE PROBLEMS [PDF]
Taiwanese Journal of Mathematics, 2010 In this paper, we establish the existence of multiple positive solutions for singular integral equations. The proof is based on a general existence principle established using a nonlinear alternative principle of Leray-Schauder type and a well-known fixed point theorem in cones.
Chu, Jifeng, O'Regan, Donal
openaire +2 more sources
Some weakly singular Volterra integral inequalities with maxima in two variables
Journal of Inequalities and Applications, 2023 In this paper, we establish some new weakly singular Volterra type integral inequalities that include the maxima of the unknown function of two variables.
Yining Sun, Run Xu
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