Results 11 to 20 of about 362 (95)
A Liapunov functional for a linear integral equation
Electronic Journal of Qualitative Theory of Differential Equations, 2010 In this note we consider a scalar integral equation $x(t)= a(t)-\int^t_0 C(t,s)x(s)ds$, together with its resolvent equation, $R(t,s)= C(t,s)-\int^t_s C(t,u) R(u,s)du$, where $C$ is convex. Using a Liapunov functional we show that for fixed $s$ then $|R(
Theodore Burton
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Integrable Solutions of a Functional-Integral Equation
Revista Matemática Complutense, 1989 Under certain assumptions on the functions f,g,k the authors prove that the functional-integral equation \[ x(t)=g(t)+f(t,\int^{1}_{0}k(t,s)x(\phi (s))ds), \] \(t\in [0,1)\) has at least one solution \(x\in L^ 1[0,1]\), which is a.e. nonincreasing on \(L^ 1[0,1]\).
Banaś, Józef, Knap, Zygmunt
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Existence of periodic solutions for a class of functional integral equation
Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this paper, we investigate the existence of periodic solution for a class of nonlinear functional integral equation. We first prove a fixed point theorem in a Banach algebra and with its help, an existence theorem about periodic solution to the ...
Wei Long, Xiong-Jun Zheng, Lu Li
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Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy
International Journal of Mathematics and Mathematical Sciences, 1991 A discussion is given of some of the properties of the functional Volterra Integral equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy. and of the corresponding multidimensional equation.
Li. G. Chambers
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Integral equations for Lamé functions [PDF]
Proceedings of the Edinburgh Mathematical Society, 1942 In the theory of ordinary linear differential equations with three regular singularities and in the theory of their special and limiting cases, integral representations of the solutions are known to be very important. It seems that there is no corresponding simple integral representation of the solutions of ordinary linear differential equations with ...
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Weighted Cauchy-type problem of a functional differ-integral equation
Electronic Journal of Qualitative Theory of Differential Equations, 2007 In this work, we are concerned with a nonlinear weighted Cauchy type problem of a differ-integral equation of fractional order. We will prove some local and global existence theorems for this problem, also we will study the uniqueness and stability of ...
Ahmed El-Sayed +1 more
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Approximation Solution of Volterra Integral Equation Using Adomian Decomposition Method [PDF]
Engineering and Technology Journal, 2009 In this paper, Adomian Decomposition method has been used to find the approximationsolution for the linear Volterra integral equation of the second kind.
Khawla A. AL-Zubaidy
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Lyapunov Functionals in Integral Equations
Axioms, 2023 Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it is therefore further explored in this paper. In this manuscript, we utilize Lyapunov functionals combined with Laplace transform to qualitatively analyze the solutions of the integral equation In ...
Youssef N. Raffoul, Joseph Raffoul
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Applications of Normal S-Iterative Method to a Nonlinear Integral Equation
The Scientific World Journal, 2014 It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.
Faik Gürsoy
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On optimal control problem for the heat equation with integral boundary condition
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2016 In this paper we consider the optimal control problem for the heat equation with an integral boundary condition. Control functions are the free term and the coefficient of the equation of state and the free term of the integral boundary condition.
Rafiq K Tagiev, Vahab M Habibov
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