This study concerns a generalized class of biharmonic-type boundary value problems with nonstandard growth conditions over bounded irregular domains. We provide a unitary treatment for various types of applied problems with variable exponents, like the $p\left(\cdot \right)$-biharmonic problems, mean curvature problems, and capillarity problems. The multiplicity result established here includes situations that cannot occur on the constant exponent case.

中文翻译：

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应用具有非标准增长结构的高阶椭圆问题

本研究涉及在有界不规则域上具有非标准增长条件的一类广义双调和型边值问题。我们为各种类型的具有可变指数的应用问题提供统一处理，例如$磷\left(\cdot \right)$-双调和问题、平均曲率问题和毛细管问题。这里建立的多重性结果包括在常数指数情况下不能发生的情况。