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A volterra-type integral equation
Ukrainian Mathematical Journal, 1989See the review in Zbl 0653.45005.
Ashirov, S., Mamedov, Ya. D.
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Eigenvalues and Nonlinear Volterra Equations
1995This paper is devoted to present a solution to the eigenvalue problem for non-linear Volterra operators having the form $$ Tu(x) = \int_0^x {k(x - s)g(u(s))} ds $$ .
Arias M., Castillo J., SIMOES, Marilda
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Stability of Volterra Difference Equations
Differential Equations, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kolmanovskii, V. B., Kosareva, N. P.
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Journal of the Physical Society of Japan, 1985
We consider a predator-prey system on a continuous rank spectrum of species. We present conjectural N-soliton solution of this system and investigate the flow of biomass caused by 1-soliton solution.
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We consider a predator-prey system on a continuous rank spectrum of species. We present conjectural N-soliton solution of this system and investigate the flow of biomass caused by 1-soliton solution.
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2012
In this chapter, our attention is devoted to the Volterra integral equation of the second kindwhich assumes the form $$\phi (x) = f(x) + \lambda \,{\int \nolimits }_{a}^{x}\,K(x,t)\,\phi (t)\,\mathrm{d}t.$$ (4.1) Volterra integral equations differ from Fredholm integral equations in that the upper limit of integration is the variable x ...
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In this chapter, our attention is devoted to the Volterra integral equation of the second kindwhich assumes the form $$\phi (x) = f(x) + \lambda \,{\int \nolimits }_{a}^{x}\,K(x,t)\,\phi (t)\,\mathrm{d}t.$$ (4.1) Volterra integral equations differ from Fredholm integral equations in that the upper limit of integration is the variable x ...
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Homogenization for a Volterra Equation
SIAM Journal on Mathematical Analysis, 1986Les AA. considèrent une équation de Volterra de la forme \[ b_ 0u- div_ x(c*\sigma)=b_ 0u_ 0-\beta *u+H \] où \(c=c(x,t)\) et \(b_ 0=b_ 0(x)\) sont des fonctions positives données, \(\sigma =\sigma (x,\nabla u(x,t))\), \(\beta =\beta (x,t)\) et \(H=H(x,t)\) sont données ainsi que \(u_ 0=u_ 0(x)\).
Attouch, Hedy, Damlamian, Alain
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Nonlinear hyperbolic volterra integrodifferential equations
Nonlinear Analysis: Theory, Methods & Applications, 1996The well posedness of the abstract Cauchy problem \[ u'(t) = Au(t) + \int^t_{t_0} K \bigl( t,s,u(s) \bigr) ds + f(t), \quad u(t_0) = u_0 \] is studied, \(A\) denoting a linear Hille-Yosida operator in the Banach space \((X,II \cdot II)\). The paper consists of different Sections, and includes the proof of various theorems. The last Section refers to an
Nagel, Rainer, Sinestrari, Eugenio
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A Volterra Equation with Parameter
SIAM Journal on Mathematical Analysis, 1973We discuss the Volterra integral equation $x'(t) + \lambda \int_0^t {a(t - \tau )x(\tau )d\tau = k,\lambda \geq \lambda _0 > 0} $. We find conditions under which solutions are bounded on $\{ 0 \leq t < \infty \} $, uniformly in $\lambda $. We deduce results on the asymptotic behavior of certain Volterra equations in Hilbert space arising, for example ...
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2017
This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels ...
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This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels ...
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