Caffarelli-Kohn-Nirenberg inequality for biharmonic equations with inhomogeneous term and Rellich potential

In this article, multiplicity of nontrivial solutions for an inhomogeneous singular biharmonic equation with Rellich potential are studied. Firstly, a negative energy solution of the studied equations is achieved via the Ekeland's variational principle and Caffarelli-Kohn-Nirenberg inequality. Then by applying Mountain pass theorem lack of Palais-Smale conditions, the second solution with positive energy is also obtained.