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On one approach to the study of the asymptotic behaviour of the Riccati equation with complex-valued coefficients. (English) Zbl 0814.34029
The Riccati equation with complex valued coefficients $z'= p(t) (a(t)- z)(b(t)- z)\tag{1}$ is considered. The asymptotic behaviour of the solutions of this equation, especially the existence of bounded solutions and of solutions satisfying conditions of the form $\lim_{t\to\infty} z(t)= a_ 0\quad\text{or}\quad \int^ \infty_{t_ 0} | z(t)- a_ 0| dt< \infty,$ is studied. The investigation is based on the reduction of the Riccati equation to the equation (2) $$z'= zg(t, z)+ h(t, z)$$. Sufficient conditions for the equation (2) to have bounded solutions (as $$t\to\infty$$) and solutions satisfying $\lim_{t\to\infty} z(t)= 0\quad\text{or}\quad \int^ \infty_{t_ 0} | z(t)| dt <\infty$ are obtained.

##### MSC:
 34D05 Asymptotic properties of solutions to ordinary differential equations 34M99 Ordinary differential equations in the complex domain
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##### References:
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