The Pohozaev-type inequalities and their applications for a kind of elliptic equation (system). (English) Zbl 1489.35148
Summary: In this paper, we first derive a new kind of Pohozaev-type inequalities for p-Laplacian equations in a more general class of non-star-shaped domains, and then we take two examples and their graphs to explain the shape of the new kind of the non-star-shaped domain. At last, we extend the results of Pohozaev-type inequalities to elliptic systems, which are used to derive the nonexistence of positive solutions of this type of systems in the non-star-shaped domains. On this basis, we also discuss the existence of positive solutions of a kind of elliptic systems with double critical growth.
MSC:
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A15 | Variational methods applied to PDEs |
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