This paper deals with the mathematical analysis of a class of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator. We are concerned both with the coercive and the noncoercive (and nonresonant) cases, which are in relationship with two associated Rayleigh quotients. The proof combines critical point theory arguments and the dual variational principle. The arguments developed in this paper can be extended to other classes of nonlinear eigenvalue problems with nonstandard growth.

中文翻译：

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非齐次Leray–Lions算子的非线性特征值问题

本文研究了由非齐次微分算子驱动的一类非线性特征值问题的数学分析。我们同时关注强制性和非强制性（非共振）情况，这与两个相关的瑞利商有关。证明结合了临界点理论论证和对偶变分原理。本文提出的论点可以推广到具有非标准增长的其他类别的非线性特征值问题。