Energy Estimates and Existence Results for a Quasilinear Periodic Boundary Value Problem

This paper focuses on the existence of solutions and energy estimates for a specific type of periodic boundary value problem. By pre cisely determining the parameter’s localization, we demonstrate the ex istence of non-zero solutions and infer the presence of multiple solutions for positive parameter values. This analysis necessitates the sublinearityof the nonlinear component at both the origin and infinity. Lastly, we present a multiplicity result along with an example. The proof relies on a local minimum theorem for differentiable functionals.