Multiplicity and minimality of periodic solutions to fourth-order super-quadratic difference systems

Abstract

In this article, we use the Nehari manifold method to study a class of fourth-order even difference systems. First, we show that there exist multiple periodic solutions to the non-autonomous system. Second, we obtain sufficient conditions to guarantee the existence of solutions with prescribed minimal periods to the autonomous system. Our results generalize the results in reference.

Keywords

• difference equations
• periodic solutions
• critical point theory
• multiplicity
• 39a23
• 49j35