文献类型：期刊文献

英文题名：Nodal solutions for the double phase problems

作者：Ji, Chao[1]; Papageorgiou, Nikolaos S.[2]

机构：[1] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China; [2] Department of Mathematics, National Technical University, Zograrou Compus, Athens, 15780, Greece

年份：2023

外文期刊名：arXiv

收录：EI(收录号：20230323560)

语种：英文

外文关键词：Variational techniques

摘要：We consider a parametric nonautonomous (p,q)-equation with unbalanced growth as follows (Table presented), in ?, where ? ? N be a bounded domain with Lispchitz boundary ??, α ∈ L∞(?)\{0}, a(z) ≥ 0 for a.e. z ∈ ?, 1 0. In the reaction there is a parametric concave term and a perturbation f(z,x). Under the minimal conditions on f(z,0), which essentially restrict its growth near zero, by employing variational tools, truncation and comparison techniques, as well as critical groups, we prove that for all small values of the parameter λ > 0, the problem has at least three nontrivial bounded solutions (positive, negative, nodal), which are ordered and asymptotically vanish as λ → 0+ ? 2023, CC BY-NC-SA.