Abstract
In this paper, we study the biharmonic operator on a manifold with conical singularities and consider the existence of non-trivial weak solution for the corresponding semilinear degenerate elliptic equation with critical cone Sobolev exponents by the cone Sobolev inequality and Poincaré inequality. Furthermore, we show an interesting integral identity, which can be used to discuss the non-existence results for some biharmonic equations under Navier boundary conditions.
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