Results 171 to 180 of about 2,297,756 (205)
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2016
In this chapter, we conducted a thorough examination of the Volterra integral equation of the second kind for an arbitrary real parameter λ, assuming that the free term f (x) is real-valued and continuous on the interval [a, b] and that the kernel K(x, t) is real-valued, continuous, and separable on the square Q(a, b) = {(x, t): [a, b] × [a, b]}.
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In this chapter, we conducted a thorough examination of the Volterra integral equation of the second kind for an arbitrary real parameter λ, assuming that the free term f (x) is real-valued and continuous on the interval [a, b] and that the kernel K(x, t) is real-valued, continuous, and separable on the square Q(a, b) = {(x, t): [a, b] × [a, b]}.
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1970
In this chapter we investigate operator equations and inequalities for functions of one real variable. Our particular objective here is nonlinear Volterra integral equations and ordinary differential equations. Unless explicitly stated otherwise, the Lebesgue concept of integral is always presupposed.
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In this chapter we investigate operator equations and inequalities for functions of one real variable. Our particular objective here is nonlinear Volterra integral equations and ordinary differential equations. Unless explicitly stated otherwise, the Lebesgue concept of integral is always presupposed.
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A Stieltjes–Volterra Integral Equation Theory
Canadian Journal of Mathematics, 1966Suppose S = [a, b] is a number interval and F is a function from S X S to a normed algebraic ring N with multiplicative identity I. We consider the problem of finding, for appropriate conditions on F, a function M from S X S to N such that for all t and x,where the integral is a Cauchy-left integral.
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On Volterra–Fredholm Equations with Partial Integrals
Differential Equations, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Asymptotic Behavior of Volterra Integral Equations
SIAM Journal on Mathematical Analysis, 1972Suppose $y(t) = f(t) - \int_0^t {a(t,s)y(s)ds} $ is a system of Volterra integral equations, and let $r(t,s)$ be the resolvent kernel corresponding to this system. If $f(t)$ is continuous and $\omega $-periodic, it is shown that under suitable restrictions on $r(t,s)$, the solution $y(t)$ is asymptotically $\omega $-periodic.
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VOLTERRA INTEGRAL EQUATIONS AND NONLINEAR SEMIGROUPS
Nonlinear Analysis: Theory, Methods & Applications, 1977Publisher Summary This chapter discusses Volterra integral equations and nonlinear semigroups. It presents the nonlinear Volterra integral equation x ( t ) = y ( t ) + ∫ g ( t − s , x ( s )) ds , t ≥ 0, where H is a Hilbert space, y : [0, ∞) → H is given, g : [0, ∞) × H → satisfies a Lipschitz condition in its second place, and x :
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On Volterra Integral Equations on Time Scales
Mediterranean Journal of Mathematics, 2014The following Volterra integral equations are considered: \[ x(t)=f(t)+\int\limits_{a}^{t} g(t,s,x(s))\Delta s \] and \[ x(t)=f(t)+\int\limits_{a}^{t} g(t,s,x(\sigma(s)))\Delta s, \] where \(x: \mathbb{T}\to \mathbb{R}^n\) is the unknown function, \(g: \mathbb{T}\times\mathbb{T}\times\mathbb{R}^n\to\mathbb{R}^n\) and \(f:\mathbb{T}\to\mathbb{R}^n\) are
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Solving Volterra integral equation by using a new transformation
Journal of Interdisciplinary Mathematics, 2021Ahmed Hadi Hussain
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Differential transform method for solving Volterra integral equation with separable kernels
Mathematical and Computer Modelling, 2008Zaid Odibat
exaly