Abstract:
By utilizing iterative method, oscillation of solutions to high-order variable coefficient functional differential equations of the form x(g(t))〖KG-*4〗=p(t)x(t)+〖DD(〗m〖〗i=1〖DD)〗Qi(t)〖DD(〗s〖〗j=1〖DD)〗〖JB(|〗x(gk_j+i(t))〖JB)|〗ajsgn x(gkj+i(t)) is discussed. When n0, n is an integer, and lim〖DD(X〗t〖DD)〗sup〖DD(〗m〖〗i=1〖DD)〗Qi(t)〖DD(〗s〖〗j=1〖DD)〗〖JB2*[〗〖DD(〗kj+i-1〖〗k=1〖DD)〗p(gk(t))〖JB2*]〗aj1〖KG0.8mm〗(t〖XC152HSW1.TIF;%85%85,JZ〗I), all the solutions of the above equations are oscillation. When n0, n is an integer, and lim〖DD(X〗t〖DD)〗sup〖JB2*[〗p(g(t))〖DD(〗m〖〗i=1〖DD)〗Qi(t)〖DD(〗s〖〗j=1〖DD)〗〖JB2*[〗〖DD(〗kj+i-2〖〗k=1〖DD)〗pn(gk(t))〖JB2*]〗j+〖DD(〗m〖〗i=1〖DD)〗Qi(g(t))〖DD(〗s〖〗j=1〖DD)〗〖JB2*[〗〖DD(〗kj+i〖〗k=2〖DD)〗pn(gk(t))〖JB2*]〗j〖JB2*]〗1〖KG1.5mm〗(t〖XC152HSW1.TIF;%85%85,JZ〗I), all the solutions of the above equations are oscillation. Some sufficient conditions for these equations are established. Some applications in difference equations are given.