# Existence of periodic solutions for semilinear parabolic equations

Norimichi Hirano; Noriko Mizoguchi

Banach Center Publications (1996)

- Volume: 35, Issue: 1, page 39-49
- ISSN: 0137-6934

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topHirano, Norimichi, and Mizoguchi, Noriko. "Existence of periodic solutions for semilinear parabolic equations." Banach Center Publications 35.1 (1996): 39-49. <http://eudml.org/doc/251308>.

@article{Hirano1996,

abstract = {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 _\{+\} × \bar\{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 → ±∞.},

author = {Hirano, Norimichi, Mizoguchi, Noriko},

journal = {Banach Center Publications},

keywords = {multiplicity of T-periodic solutions},

language = {eng},

number = {1},

pages = {39-49},

title = {Existence of periodic solutions for semilinear parabolic equations},

url = {http://eudml.org/doc/251308},

volume = {35},

year = {1996},

}

TY - JOUR

AU - Hirano, Norimichi

AU - Mizoguchi, Noriko

TI - Existence of periodic solutions for semilinear parabolic equations

JO - Banach Center Publications

PY - 1996

VL - 35

IS - 1

SP - 39

EP - 49

AB - 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 _{+} × \bar{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 → ±∞.

LA - eng

KW - multiplicity of T-periodic solutions

UR - http://eudml.org/doc/251308

ER -

## References

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