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Zbl 1125.34024
Sun, Yuan Gong; Wong, James S.W.
Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities. (English)
[J] J. Math. Anal. Appl. 334, No. 1, 549-560 (2007). ISSN 0022-247X

The authors introduce general oscillation criteria for the second order ordinary differential equation $$ \big(p(t)\,x'\big)'+q(t)\,x+\sum_{i=1}^nq_i(t)\,\vert x\vert ^{\alpha_1}\,\mathrm{sgn}\,x=e(t), $$ where $p,q,q_i,e\in C[0,\infty)$, $p(t)>0$ and differentiable (but this assumption on the existence of $p'(t)$ is apparently not needed), $\alpha_1>\dots>\alpha_m>1>\alpha_{m+1}>\dots>\alpha_n$, and no restriction is invoked on the forcing term $e(t)$. Note that the equation contains both sublinear and superlinear terms due to the assumptions on the exponents $\alpha_i$. The main results (Theorems~1--3) are derived via the Riccati technique and generalize several results in the literature.
[Roman Hilscher (Brno)]

MSC 2000:: *34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: Forced oscillation; Nonlinear differential equation

Cited in: Zbl 1240.34310 Zbl 1217.34055 Zbl 1193.35055 Zbl 1173.35485

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