On the \(L^{2}_{w}\)-boundedness of solutions for products of quasi-integro differential equations (Q1864301)

The author considers general quasidifferential expressions \(\tau_1, \tau_2,\dots , \tau_n\), each of the order \(n\) with in general complex coefficients and their formal adjoint ones \(\tau_1^+, \tau_2^+,\dots, \tau_n^+\) on \([0, b)\) with \( 0 < b\leq \infty\). Under some restrictions, it is shown that all solutions to the product of the quasi-integrodifferential equation \[ \Biggl[\prod_{j=1}^n \tau_j\Biggr] y = w F\Biggl(t,y, \int_0^t g(t, s, y, y', \dots y^{(n^2-1)}(s)) ds\Biggr) \] with given \(F\) and \(w\) are bounded and \(L_w^2\) -bounded.