On systems of elliptic equations involving subcritical or critical Sobolev exponents
Existence and non-existence results of positive solutions for a system of elliptic equations with Dirichlet boundary data in a bounded domain with smooth boundary are considered. A non-existence result is proved when \(\Omega\) is star shaped, using some type of Pohozaev identity for a system. Many comparisons with the corresponding scalar case of the problem treated by \textit{H. Brezis} and {L. Nirenberg} [Commun. Pure Appl. Math. 36, 437-477 (1983; Zbl 0541.35029)] are given.
scientific article; zbMATH DE number 1513294