Generalized averages for solutions of nonlinear systems

The average of nonzero solutions of second-order ordinary differential system x′ = −|y|2q−2y, y′ = f(x), x(t1) = x(t2) = 0 are obtained if 2q > 1, f(x) ϵ C1 (R,R), and uf(u) > 0 for u > 0 is obtained.