Displaying similar documents to “Periodic segments and Nielsen numbers”

Partially dissipative periodic processes

Jan Andres, Lech Górniewicz, Marta Lewicka (1996)

Banach Center Publications

Similarity:

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.

Periodic Solutions of Periodic Retarded Functional Differential Equations

Marcin Pawłowski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (RFDE) x ' ( t ) = f ( t , x t ) , where f is T-periodic in t. We construct a pair of subsets of ℝ × ℝⁿ called a T-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a T-periodic solution.

Existence of periodic solutions for semilinear parabolic equations

Norimichi Hirano, Noriko Mizoguchi (1996)

Banach Center Publications

Similarity:

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 → ±∞.