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Nontrivial solution of some semilinear cooperative elliptic systems with critical Sobolev exponent. (English) Zbl 1142.35430

Summary: This paper deals with the existence of nontrivial solutions of some semilinear cooperative elliptic systems involving critical Sobolev exponent. It is well-known that one of the most important problem of elliptic systems is to find the really nontrivial solution. Under some conditions we obtain the existence of a nontrivial solution by analyzing the best Sobolev embedding constant and by use of the minimax theorems without (PS) conditions. In fact, the solution we obtain here is really nontrivial in the sense of unknown functions being nontrivial.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
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