1. On the asymptotic behavior at infinity of solutions to quasi-linear differential equations
- Creator:
- Astashova, Irina
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- quasi-linear ordinary differential equation of higher order, existence of non-oscillatory solution, and oscillatory solution
- Language:
- English
- Description:
- Sufficient conditions are formulated for existence of non-oscillatory solutions to the equation y (n) + ∑ n−1 j=0 aj (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 aj (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 for existence of solution to this equation which is equivalent to a polynomial.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public