Abstract
We consider the equation u″=P(z)u+F(z) (z∈C), where P(z) is a polynomial and F(z) is an entire function. Let zk(u), k=1, 2, . . ., be the zeros of a solution u(z) to that equation. Estimates for the sums ∑k=1j1|zk(u)| (j=1, 2, . . .) are derived. In particular, they give us bounds for the zero free domain. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed.
Original language | English |
---|---|
Pages (from-to) | 1917-1924 |
Number of pages | 8 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 421 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jan 2015 |
Keywords
- ODE in the complex plane
- Zeros of solutions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics