Displaying similar documents to “Harmonic solutions to perturbations of periodic separated variables ODEs on manifolds.”

Existence of periodic solutions for semilinear parabolic equations

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 ( 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 → ±∞.