Infinitely many solutions for double harmonic perturbed problem (Q1904860)

The author proves the existence of infinitely many nontrivial solutions of the problem \[ \Delta^2 u- a\Delta u+ bu= g(x, u)+ f(x, u)\text{ in }\Omega,\;u= \partial u/\partial n= 0\text{ on }\partial\Omega, \] under several growth conditions on \(g\) and \(f\), for \(a\geq 0\), \(b\geq 0\). The proof uses variational methods and index theories on Banach manifolds.