Existence of positive periodic solutions for non-autonomous functional differential equations.
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Electronic Journal of Differential Equations (EJDE) [electronic only]
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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 u = 0 if , where is a bounded domain with smooth boundary ∂Ω and 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 → ±∞.