ABSTRACT

In this paper we obtain an existence result for an wide class of problems involving variable exponents which are related to several applications in electrorheological fluids and image processing. Under additional conditions it is obtained the multiplicity of solutions. It is also presented examples of applicability of the results. The arguments are based on sub-supersolutions and appropriated $L^{\mathrm{\infty }}$ estimates in the variable spaces setting.

中文翻译：

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涉及 p(x)-拉普拉斯算子的一​​类问题的多种解决方案

摘要

在本文中，我们获得了涉及变指数的一大类问题的存在性结果，这些问题与电流变流体和图像处理中的几种应用有关。在附加条件下，得到解的多样性。它还提供了结果适用性的示例。论点是基于子超解和适当的${\mathrm{大号}}^{\mathrm{\infty }}$变量空间设置中的估计值。