On the existence and multiplicity of positive periodic solutions of a nonlinear third-order equation

In this paper, we are concerned with the existence and multiplicity of positive 2 π -periodic solutions for the following nonlinear third-order problem u ‴ ( t ) + α u ″ ( t ) + β u ′ ( t ) = f ( t , u ( t ) ) . Here α , β are two positive constants, f ( t , u ) ∈ C ( R × R , R ) , f ( t + 2 π , u ) = f ( t , u ) . The proof relies on a fixed point theorem on cones.