We prove existence results in all of \({\mathbb {R}}^N\) for an elliptic problem of (p, q)-Laplacian type involving a critical term, nonnegative weights and a positive parameter \(\lambda \). In particular, under suitable conditions on the exponents of the nonlinearity, we prove existence of infinitely many weak solutions with negative energy when \(\lambda \) belongs to a certain interval. Our proofs use variational methods and the concentration compactness principle. Towards this aim we give a detailed proof of tight convergence of a suitable sequence.

中文翻译：

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（p，q）-Laplacian方程的多重结果，其临界指数为$$ {\ mathbb {R}} ^ N $$ RN且能量为负

我们证明了（p，  q）-Laplacian型椭圆问题涉及一个关键项，非负权重和一个正参数\（\ lambda \）的所有\（{\ mathbb {R}} ^ N \）的存在结果。特别是，在非线性指数的适当条件下，当\（\ lambda \）属于某个区间时，我们证明存在带有负能量的无穷多个弱解。我们的证明使用变分方法和浓度压缩原理。为了达到这个目的，我们给出了适当序列紧密收敛的详细证明。