Non-existence Results And Existence Results For The Elliptic Equations

In this paper, we mainly study three nonlinear elliptic equations .Inchapter 2,we obtain some non-existence results for the Klein-Gordon-Born-Infeldequations.The method relies on the deduction of some suitable Pohoˇzaev iden-tity which provides necessary conditions to get existence of nontrivial solutions;In chapter 3, we obtain some non-existence results for a non-cooperative ellipticsystem with lack of compactness; In chapter 4, we obtain infinitely many radi-ally symmetric solutions of a semilinear cooperative system on the unboundeddomain .The method relies on Z₂ version of the mountain pass theorem.