Oscillation theorems of nonlinear Volterra-Stieltjes integral equations
The oscillatory behavior of solutions to the nonlinear Volterra-Stieltjes integral equation \[ p(t) \psi (y) y'_+ (t)= c+ \int^t_0 f(y (s)) d\sigma (s) \] is considered. \(y'_+ (t)\) denotes the right derivative of \(y(t)\), \(p(t)> 0\) and \(\sigma (t)\) are right-continuous and of locally bounded variation on \([0, \infty)\), \(\psi: (- \infty, \infty)\to [0, \infty)\) is a continuous and \(f: (- \infty, \infty)\to (- \infty, \infty)\) is a continuously differentiable function. Some properties for the non-oscillatory solution are also given.
nonlinear Volterra-Stieltjes integral equations
scientific article; zbMATH DE number 861838