Fan, Zi’an; Kou, Jisheng Existence of nontrivial solutions of the semilinear cooperative elliptic systems involving subcritical Sobolev exponents. (Chinese. English summary) Zbl 1413.35177 J. North Univ. China, Nat. Sci. 38, No. 6, 576-581 (2017). Summary: The cooperative semilinear elliptic system involving subcritical Sobolev exponents was investigated. The existence of nontrivial solution to the system was obtained under different cases. In the case \(0 < \lambda < \lambda_1 \), through defining the functional and the corresponding Nehari manifold, we got that the functional \(J (u, v)\) was bounded below. Then we proved that the functional had a minimizer, so the functional had a nontrivial critical point in the Nehari manifold and the problem had a nontrivial solution in \(E\). In the case \({\lambda_k} < \lambda < {\lambda_{k + 1}}\), the functional satisfied the conditions of local linking theorem. It is concluded that there exists at least one nontrivial solution. MSC: 35J46 First-order elliptic systems 35J61 Semilinear elliptic equations Keywords:subcritical Sobolev exponents; cooperative elliptic systems; Nehari manifold; local linking theorem PDFBibTeX XMLCite \textit{Z. Fan} and \textit{J. Kou}, J. North Univ. China, Nat. Sci. 38, No. 6, 576--581 (2017; Zbl 1413.35177) Full Text: DOI