Existence and uniqueness of solution to a fourth-order Kirchhoff type elliptic equation with strong singularity
Volume 130 / 2023
Annales Polonici Mathematici 130 (2023), 253-269
MSC: Primary 35J75; Secondary 35J30.
DOI: 10.4064/ap220727-1-3
Published online: 23 March 2023
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 $H_0^2(\Omega )$, 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.
