Displaying similar documents to “A survey of Nielsen periodic point theory (fixed n)”

Partially dissipative periodic processes

Jan Andres, Lech Górniewicz, Marta Lewicka (1996)

Banach Center Publications

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Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.

Existence of periodic solutions for semilinear parabolic equations

Norimichi Hirano, Noriko Mizoguchi (1996)

Banach Center Publications

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In this paper, we are concerned with the semilinear parabolic equation ∂u/∂t - Δu = g(t,x,u) if ( t , x ) ∈ R + × Ω u = 0 if ( t , x ) ∈ R + × ∂ Ω , where Ω ⊂ R N is a bounded domain with smooth boundary ∂Ω and g : R + × Ω ¯ × R → R is T-periodic with respect to the first variable. The existence and the multiplicity of T-periodic solutions for this problem are shown when g(t,x,ξ)/ξ lies between two higher eigenvalues of - Δ in Ω with the Dirichlet boundary condition as ξ → ±∞.

Periodic solutions for a class of functional differential system

Weibing Wang, Baishun Lai (2012)

Archivum Mathematicum

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In this paper, we study the existence of periodic solutions to a class of functional differential system. By using Schauder's fixed point theorem, we show that the system has aperiodic solution under given conditions. Finally, four examples are given to demonstrate the validity of our main results.