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On the asymptotic behavior at infinity of solutions to quasi-linear differential equations

Irina Astashova (2010)

Mathematica Bohemica

Sufficient conditions are formulated for existence of non-oscillatory solutions to the equation y ( n ) + j = 0 n - 1 a j ( x ) y ( j ) + p ( x ) | y | k sgn y = 0 with n 1 , real (not necessarily natural) k > 1 , and continuous functions p ( x ) and a j ( x ) defined in a neighborhood of + . For this equation with positive potential p ( x ) 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...

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