Existence of periodic solutions for p-Laplacian equation without growth restrictions


In this paper, we deal with the nonlinear fully second-order differential equation with p-Laplacian

$$\begin{aligned} (\phi _p(x'))'=f(t,x,x'),\quad t\in \mathbb {R}:=(-\infty ,\infty ), \end{aligned}$$

where \(\phi _p(s)=|s|^{p-2}s\), \(p>1\), function \(f:\mathbb {R}^3 \rightarrow \mathbb {R}\) is continuous and T-periodic with respect to t. Using the topological transversality method and the barrier strip technique, we obtain new existence results of periodic solutions to the above p-Laplacian equation without growth restrictions. Meanwhile, an application is given for the Rayleigh-type p-Laplacian equation.

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The authors thank the referee for valuable suggestions, which led to improvement of the original manuscript.

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Correspondence to Libo Wang.

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Pei, M., Wang, L. Existence of periodic solutions for p-Laplacian equation without growth restrictions. Z. Angew. Math. Phys. 72, 53 (2021). https://doi.org/10.1007/s00033-021-01486-x

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  • p-Laplacian equation
  • Periodic solution
  • Topological transversality
  • Barrier strip

Mathematics Subject Classification

  • 34B15
  • 34C25