Bahaguna, D.; Pani, A. K.; Raghavendra, V. Rothe’s method to semilinear hyperbolic integrodifferential equations. (English) Zbl 0721.45007 J. Appl. Math. Stochastic Anal. 3, No. 4, 245-252 (1990). 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. Reviewer: A.Pil’kevich (Kiev) Cited in 5 Documents MSC: 45N05 Abstract integral equations, integral equations in abstract spaces 45J05 Integro-ordinary differential equations 45L05 Theoretical approximation of solutions to integral equations Keywords:Rothe’s method; abstract semi-linear hyperbolic integrodifferential equations; Hilbert spaces; positive definite operator; V-elliptic operator; Lax-Milgram lemma; uniqueness; existence; strong solution PDFBibTeX XMLCite \textit{D. Bahaguna} et al., J. Appl. Math. Stochastic Anal. 3, No. 4, 245--252 (1990; Zbl 0721.45007) Full Text: DOI EuDML