ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES

In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations contain nonlinear monotone operators and a nonmonotone perturbation. Moreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of secondorder nonlinear evolution equations is verified. Our abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.