In this work we obtain three radial solutions of a biharmonic stationary Schrodinger equation, one being positive, one negative, and one sign changing. The dual decomposition method is used to split the natural second-order Sobolev space considered in order to apply the appropriate variational approach.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)