Fixed points and stability of a class of integrodifferential equations (Q1718047)

Summary: We study a class of integrodifferential functional differential equations \(\ddot{x} + f(t, x, \dot{x}) \dot{x} + \sum_{j = 1}^N \int_{t - r_j(t)}^t a_j(t, s) g_j(s, x(s)) d s = 0\) with variable delay. By using the fixed point theory, we establish necessary and sufficient conditions ensuring that the zero solution of this equation is asymptotically stable.