We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator, which includes as a particular case the scalar p-Laplacian. We assume that the reaction is a Carathéodory function which admits time-dependent zeros of constant sign. No growth control near ±∞ is imposed on the reaction. Using variational methods coupled with suitable truncation and comparison techniques, we prove two multiplicity theorems providing sign information for all the solutions.

中文翻译：

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非线性，非齐次周期问题，没有反应的增长控制。

我们考虑由非齐次微分算子驱动的非线性周期问题，在特定情况下，该问题包括标量p -Laplacian。我们假设该反应是一个Carathéodory函数，该函数接受常数符号随时间变化的零。在反应上没有施加接近±∞的生长控制。使用变分方法，再加上适当的截断和比较技术，我们证明了两个多重性定理，它们为所有解提供符号信息。