Infinitely many solutions for double harmonic perturbed problem
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.
semilinear elliptic equation of fourth order
scientific article; zbMATH DE number 833494
scientific article