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On Volterra-Stieltjes integral equations [PDF]
Časopis pro pěstování matematiky, 1974 openaire +2 more sources
On a nonlinear Volterra equation of nonconvolution type
, 1979 Manfred C Smith
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Stieltjes-Volterra integral equations
Illinois Journal of Mathematics, 1970 openaire +3 more sources
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On a nonlinear volterra equation
Mathematical Methods in the Applied Sciences, 1986AbstractNonnegative solutions u of the nonlinear Volterra equation u = a * g(u) (g(0) = 0) in mathematical physics are considered. Under certain assumptions the nonhomogenuous equation u = a * g(u) + ƒ is studied. Some approximations of nonnegative solutions of the homogenuous equation are considered by the nonnegative solutions of the nonhomogenuous ...
W. Okrasiński Wroclaw, E. Meister
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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 \(u_ 0=u_ 0(x)\).
Hedy Attouch, Alain Damlamian
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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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Journal of Soviet Mathematics, 1979
One presents a survey of the investigations in the theory of Volterra integral equations, reviewed in Ref. Zh. “Mat.” between 1966–1976.
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One presents a survey of the investigations in the theory of Volterra integral equations, reviewed in Ref. Zh. “Mat.” between 1966–1976.
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On a diffusion volterra equation
Nonlinear Analysis: Theory, Methods & Applications, 1979INTRODUCTION IN THIS paper we study the Volterra diffusion equation au/at = Au + au bu2 u(f*u)t (0.1 a) describing the evolution of some population governed by the intrinsic rate a bu and the memory rate f * u containing the effect of the past history on the actual population development.
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1971
Consider the system $${\rm{A\:x}}\left( {\rm{t}} \right) + {\rm{Bx}}\left( {\rm{t}} \right) = \int_0^{\rm{r}} {{\rm{F}}\left( \theta \right){\rm{x}}\left( {{\rm{t}} - \theta } \right)} {\rm{d}}\theta $$ (15.1) where A,B,F are symmetric n × n matrices and F is continuously differentiable. Let $${\rm{M}} = {\rm{B}} - \int_0^{\rm{r}} {{\rm{F}
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Consider the system $${\rm{A\:x}}\left( {\rm{t}} \right) + {\rm{Bx}}\left( {\rm{t}} \right) = \int_0^{\rm{r}} {{\rm{F}}\left( \theta \right){\rm{x}}\left( {{\rm{t}} - \theta } \right)} {\rm{d}}\theta $$ (15.1) where A,B,F are symmetric n × n matrices and F is continuously differentiable. Let $${\rm{M}} = {\rm{B}} - \int_0^{\rm{r}} {{\rm{F}
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On controllability for a nonlinear Volterra equation [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 1990 Summary: We consider the following nonlinear Volterra wave equation with a control function \(h(t)\): \[ u_{tt}=u_{xx}-\int^ t_ 0 k(t,s)f(u(s,x))dx+b(x)h(t),\quad ...
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