We investigate a more general nonlinear biharmonic equation
where is the biharmonic operator, , and are parameters, with . Differently from previous works on biharmonic problems, we replace Laplacian with -Laplacian, and suppose that with and can be singular at the origin, in particular we allow to be a real number. Under suitable conditions on and , the multiplicity of solutions is obtained for sufficiently large. Our analysis is based on variational methods as well as the Gagliardo–Nirenberg inequality.
"Multiple solutions for generalized biharmonic equations with singular potential and two parameters." Rocky Mountain J. Math. 50 (4) 1355 - 1368, August 2020. https://doi.org/10.1216/rmj.2020.50.1355