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In this paper, the E + -Conley index theory has been used to study the existence of periodic solutions of nonautonomous delay differential equations (in short, DDEs). The variational structure for DDEs is built, and the existence of periodic solutions of DDEs is transferred to that of critical points of the associated function. When DDEs are 2 π -nonresonant, some sufficient conditions are obtained to guarantee the existence of periodic solutions. When the system is 2 π -resonant at infinity, by making use a second disturbing of the original functional, some sufficient conditions are obtained to guarantee the existence of periodic solutions to DDEs. [ABSTRACT FROM AUTHOR]

In this paper, we study the multiplicity of periodic solutions for a class of fourth-order difference equations. We estimate a lower bound on the number of periodic solutions when the nonlinearity is asymptotic both at the origin and at infinity. Our results generalize the reference' results. [ABSTRACT FROM AUTHOR]