Displaying 341 – 360 of 491

Showing per page

On the oscillation of a class of linear homogeneous third order differential equations

N. Parhi, P. Das (1998)

Archivum Mathematicum

In this paper we have considered completely the equation y ' ' ' + a ( t ) y ' ' + b ( t ) y ' + c ( t ) y = 0 , ( * ) where a C 2 ( [ σ , ) , R ) , b C 1 ( [ σ , ) , R ) , c C ( [ σ , ) , R ) and σ R such that a ( t ) 0 , b ( t ) 0 and c ( t ) 0 . 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.

On the Poincaré-Lyapunov constants and the Poincare series

Jaume Giné, Xavier Santallusia (2001)

Applicationes Mathematicae

For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare-Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial...

Currently displaying 341 – 360 of 491