Existence of Solutions to a Class of Navier Boundary Value Problem Involving the Polyharmonic

摘要

This paper is devoted to the following high order elliptic problems under the Navier boundary condition: src="Edit_c3efaa27-75c6-47d4-922d-8651d6643004.bmp" alt="" />>> style="font-family:""> style="font-family:Verdana;">?Without assuming the standard subcritical polynomial growth condition ensuring the compactness of a bounded (P.S.) sequence, we show that the Navier boundary value problem has at least a weak nontrivial solution for all style="color:#333333;font-family:Verdana;">λ style="color:#333333;font-family:Verdana;">> style="font-family:Verdana;"> style="font-family:Verdana;">0>> style="font-family:Verdana;">?by using mountain pass theorem.