Existence of oscillatory and nonoscillatory solutions for a nonlinear system of differential equations


Jelena Manojlović




We shall establish sufficient conditions for the existence of at least one nonoscillatory solution and for oscillation of all solution of the following system of differential equations \[ u'_i=|u_{3-i}|^{ambda_i}peratorname{sgn}u_{3-i}+(-1)^{i-1}b_i(t)u_i\quad(i=1,2),\quadambda_1ambda_2eq1. \]