## On Kneser solutions of nonlinear third-order differential equations.(English)Zbl 0995.34025

The paper concerns the third-order differential equation $$y'''(t)+q(t)y'(t)+f(y(t))=0$$ on $$[0,+\infty)$$. Existence and asymptotic behaviour of Kneser solutions $$y$$ are investigated, which are either positive, decreasing, and convex, or negative, increasing, and concave on some $$[t_y,+\infty)$$. A typical hypothesis states that the second-order auxiliary equation $$y''(t)+q(t)y(t)=0$$ is nonoscillatory.

### MSC:

 34C11 Growth and boundedness of solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations
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### References:

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