Periodic Solutions for Nonlinear Systems withp-Laplacian-Like Operators

Periodic solutions for nonlinear systems with mean curvature-like operators

“…We would stress that the results presented here complement those obtained in [5], since we study a class of operators not included in the setting of problems tackled by Manásevich and Mawhin. In particular, referring to [5], an operator φ satisfying the above (H1) does not verify the assumption (H 2 ) in [5] (page 369).…”

“…Bereanu and Mawhin follow a topological approach based on the Leray-Schauder degree (analogously to [5]), and, to this purpose, they find interesting a priori estimates involving the function f and the operator φ.…”

“…In [5] (see also [6]) Manásevich and Mawhin proved an existence result for the periodic boundary value problem    (φ(u )) = f (t, u, u ) u(0) = u(T ) u (0) = u (T ),…”

“…They used a topological method: the properties of φ and f allowed to apply the Leray-Schauder degree to prove that (1.1) admits a solution (see [5,Theorem 3.1]). In [1], proceeding in the general spirit of Manásevich-Mawhin's ideas, we proved an existence result for a different scalar problem.…”

“…In particular, referring to [5], an operator φ satisfying the above (H1) does not verify the assumption (H 2 ) in [5] (page 369).…”