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Boundedness of solutions for nonlinear oscillations. (English) Zbl 1030.34036

Summary: The boundedness of all the solutions to the nonlinear equation \[ \bigl(\varphi_p(x')\bigr)'+\alpha\varphi_p(x^+)-\beta \varphi_p(x^-) +f(x)=e(t) \] is proved, where \(\alpha^{-1/p} +\beta^{-1/p}= 2w^{-1}\), \(w\in\mathbb{R}^+ \setminus Q\), \(f\) is bounded, \(e(t)\in C^6\) is \(2\pi_p\)-periodic.

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
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