Comparison and nonoscillation results for Volterra-Stieltjes integral equations (Q1099366)

Conditions for exitence of nonoscillatory solutions to the equation \[ (1)\quad A(t)y'(t)=c_ 1-\int^{t}_{a}f(y(s))d\sigma_ 1(s) \] and oscillatory solutions to the equations (1) and (2) (comparison theorem) \((2)\quad a(t)y'(t)=c_ 2-\int^{t}_{a}f(y(s))d\sigma_ 2(s)\) are given. y'(t) denotes the right derivative of y(t), \(c_ 1\) and \(c_ 2\) are constants and \(\sigma_ 1\), \(\sigma_ 2\) are right-continuous and of locally bounded variation on \([t_ 0,\infty)\).