Periodic solution for a plate operator Original Research Article

In this paper we investigate periodic solutions in tt for a nonlinear plate operator View the MathML sourceL(u)=u″+Δ2u+k(x,t)|u′|p−2u′p≥2. Turn MathJax on We apply the method of Prodi [G. Prodi, Soluzioni Periodiche de l’equazioni della onde con terme dissipative non linéaire, Rend. Sem. Mat. Padova 35 (1968) 38–49] and the elliptic regularization of Lions [J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris, 1969, (Nouvelle Présentation Dunod 2002)] plus the monotony methods of Browder [F.E. Browder, Problems Non Linéaires, Press de L’Universite de Montreal, 1966]. We represent the Laplace operator by ΔΔ.