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Existence of periodic solutions for semilinear parabolic equations

Norimichi HiranoNoriko Mizoguchi — 1996

Banach Center Publications

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 → ±∞.

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