×

Existence of nontrivial solutions of the semilinear cooperative elliptic systems involving subcritical Sobolev exponents. (Chinese. English summary) Zbl 1413.35177

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
PDFBibTeX XMLCite
Full Text: DOI