In this paper first we consider eigenvalue problems for the weighted $(p,q)$-Laplacian and prove the existence of a continuous spectrum and determine its infimum. Then we deal with perturbations of the eigenvalue problem. We consider the case of sublinear and superlinear perturbations.

中文翻译：

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特征值问题及其对加权的扰动 $（p，q）$-拉普拉斯语

在本文中，我们首先考虑加权的特征值问题 $（p，q）$-Laplacian并证明连续光谱的存在并确定其最小。然后，我们处理特征值问题的摄动。我们考虑亚线性和超线性摄动的情况。