Existence of periodic solutions for semilinear parabolic equations

Hirano, Norimichi; Mizoguchi, Noriko

Banach Center Publications, Tome 37 (1996), p. 39-49 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, we are concerned with the semilinear parabolic equation ∂u/∂t - Δu = g(t,x,u) if $(t, x) \in R_{+} \times Ω$ u = 0 if $(t, x) \in R_{+} \times \partial Ω$ , where $Ω \subset R^{N}$ is a bounded domain with smooth boundary ∂Ω and $g : R_{+} \times \bar{Ω} \times R \to R$ 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 → ±∞.

Publié le : 1996-01-01

Zbl 0851.35068

EUDML-ID : urn:eudml:doc:251308

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     author = {Hirano, Norimichi and Mizoguchi, Noriko},
     title = {Existence of periodic solutions for semilinear parabolic equations},
     journal = {Banach Center Publications},
     volume = {37},
     year = {1996},
     pages = {39-49},
     zbl = {0851.35068},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv35i1p39bwm}
}

Hirano, Norimichi; Mizoguchi, Noriko. Existence of periodic solutions for semilinear parabolic equations. Banach Center Publications, Tome 37 (1996) pp. 39-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv35i1p39bwm/

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