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Non-existence results for the coupled Klein-Gordon-Maxwell equations. (English) Zbl 1142.35406

Summary: We obtain some non-existence results for the Klein-Gordon equation coupled with the electrostatic field. The method relies on the deduction of some suitable Pokhozhaev identity which provides necessary conditions to get existence of nontrivial solutions. The case of Maxwell-Schrödinger type coupled equations is also considered

MSC:

35J60 Nonlinear elliptic equations
35Q51 Soliton equations
35Q60 PDEs in connection with optics and electromagnetic theory
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