Existence and uniqueness of solution to a fourth-order Kirchhoff type elliptic equation with strong singularity

We consider the existence and uniqueness of solution to a fourth-order Kirchhoff type elliptic equation with strong singularity. By using Ekeland’s variational principle in suitable subsets of $H_0^2(\Omega )$, we obtain a necessary and sufficient condition for the existence of weak solutions. Uniqueness of weak solution is also obtained mainly by applying the monotonicity of the operator.