On stability and instability of the roots of the oscillatory function in a certain nonlinear differential equation of the third order
Sufficient conditions are formulated for existence of non-oscillatory solutions to the equation with , real (not necessarily natural) , and continuous functions and defined in a neighborhood of . For this equation with positive potential a criterion is formulated for existence of non-oscillatory solutions with non-zero limit at infinity. In the case of even order, a criterion is obtained for all solutions of this equation at infinity to be oscillatory. Sufficient conditions are obtained...