Existence of anti-periodic solutions for second-order ordinary differential equations involving the Fu?ík spectrum

摘要

In this paper, we study the existence of anti-periodic solutions for a second-order ordinary differential equation. Using the interaction of the nonlinearity with the Fu?ík spectrum related to the anti-periodic boundary conditions, we apply the Leray-Schauder degree theory and the Borsuk theorem to establish new results on the existence of anti-periodic solutions of second-order ordinary differential equations. Our nonlinearity may cross multiple consecutive branches of the Fu?ík spectrum curves, and recent results in the literature are complemented and generalized.