We investigate the existence of a nontrivial nonnegative solution to $(p,q)$-Laplace equations involving two nonlinear terms, one grows as $s$ with $q<s<p$ and the other possibly has critical growth. This interesting case cannot be appeared in single $m$-Laplace equations and has not been studied under even the subcritical growth. Our argument is based on the concentration–compactness principle by P.L. Lions and the Ekeland variational principle.

中文翻译：

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存在的结果 $（p，q）$-涉及夹心型和临界增长的拉普拉斯方程

我们调查了一个非平凡非负解的存在 $（p，q）$-涉及两个非线性项的拉普拉斯方程，一个随着 $s$ 与 $q<s<p$另一个可能有关键的增长。这个有趣的案例不能单出现$米$-Laplace方程，甚至在亚临界增长下也没有进行研究。我们的论点是基于PL Lions的浓度-紧致原理和Ekeland变分原理。