On the existence of square integrable solutions and their derivatives to fourth and fifth order differential equations
2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.Factorization is an important and very difficult problem in mathematics. Finding prime factors of a given positive integer n, or finding the roots of the polynomials in the complex plane are some of the important problems not only in algorithmic mathematics but also in cryptography.
The Cauchy problem for the system of linear generalized ordinary differential equations in the J. Kurzweil sense , with a unique solution is considered....
In this paper we have considered completely the equation where , , and such that , and . It has been shown that the set of all oscillatory solutions of (*) forms a two-dimensional subspace of the solution space of (*) provided that (*) has an oscillatory solution. This answers a question raised by S. Ahmad and A. C. Lazer earlier.