Abstract
Quasilinear boundary value problems with periodic conditions have been extensively investigated because of their importance in nonlinear analysis, mechanics, and dynamical systems. In this paper, we examine a class of second-order quasilinear differential equations with derivative-dependent principal part and periodic boundary conditions. Under a framework of structural and growth assumptions, we prove the existence of infinitely many weak solutions. Our approach is variational and based on Ricceri’s infinite critical points theorem, which ensures the existence of an unbounded sequence of critical points of the associated energy functional. The obtained results generalize and complement recent contributions in the literature concerning one, two, and three-solution problems. Several corollaries and examples are also presented to illustrate the applicability of the main theorem.