The Pohozaev-type inequalities and their applications for a kind of elliptic equation (system)

Abstract

Abstract 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.

Keywords

• Pohozaev-type inequality
• p-Laplacian
• Non-star-shaped domain
• Variational methods
• Nonexistence and existence
• Double critical exponent