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Keywords:
half-linear differential equations
half-linear differential equations
Summary:
A second-order half-linear ordinary differential equation of the type $$(|y^{\prime}|^{\alpha-1}y^{\prime})^{\prime}+\alpha q(t)|y|^{\alpha-1}y=0 \leqno{{\rm (1)}}$$ is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established.
References:
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[2] Elbert Á.: Oscillation and nonoscillation theorems for some non-linear ordinary differential equations. Lecture Notes in Mathematics (Springer), Vol. 956 (1982), 187 - 212. MR 0693113
[3] E. Hille: Lectures on Ordinary Differential Equations. Addison-Wesley, Reading, Massachusetts (1969). MR 0249698 | Zbl 0179.40301
[4] Li H. J., Yeh C. C.: Sturmian comparison theorem for half-linear second order differential equations. Proc. Royal Soc. Edinburgh 125A (1995), 1193 - 1204. MR 1362999 | Zbl 0873.34020
[5] Piros M.: On the solutions of a half-Linear differential equation. Studia Sci. Math. Hungar., 19 (1984), 193 - 211. MR 0874484 | Zbl 0638.34024
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