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

ANNALES POLONICI MATHEMATICI（2023）

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Abstract

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 Ho (ohm), 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.

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Key words

fourth-order equation,Ekeland?s variational principle,strong singularity,Kirchhoff type

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