Bounds of solutions of integrodifferential equations (Q554914)

Summary: Some new integral inequalities are given, and bounds of solutions of the following integro-differential equation are determined: \(x'(t) - \mathcal F (t, x(t), \int_0^t k(t, s, x(t), x(s))ds) = h(t)\), \(x(0) = x_0\), where \(h : \mathbb{R}_+ \rightarrow \mathbb{R}\), \(k : \mathbb{R}^2_+ \times \mathbb{R}^2 \rightarrow \mathbb{R}\), \(\mathcal F : \mathbb{R}_+ \times \mathbb{R}^2 \rightarrow \mathbb{R}\) are continuous functions, \(\mathbb{R}_+ = [0, \infty)\).