In this paper, we study a class of double-phase problems with sub-critical growth. Some new criteria to guarantee that the existence and multiplicity results for the considered problem is established by using variational methods and critical point theory.

中文翻译：

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具有亚线性和超线性非线性的双相问题

在本文中，我们研究了一类具有亚临界增长的双阶段问题。通过使用变分方法和临界点理论，建立了一些新的准则来确保所考虑问题的存在性和多重性结果。