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Rothe’s method to semilinear hyperbolic integrodifferential equations. (English) Zbl 0721.45007

The existence of a unique strong solution of the integrodifferential equation \(\frac{d^ 2u}{dt^ 2}(t)+Au(t)=\int^{t}_{0}a(t- s)k(s,u(s))ds+f(t),\) \(u(0)=U_ 0,\quad \frac{du}{dt}(0)=U_ 1\) in Hilbert spaces has been established.

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
45J05 Integro-ordinary differential equations
45L05 Theoretical approximation of solutions to integral equations
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