Existence of multiple periodic solutions for a semilinear evolution equation

Hirano, Norimichi

doi:10.1090/S0002-9939-1989-0953007-5

Existence of multiple periodic solutions for a semilinear evolution equation
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Proc. Amer. Math. Soc. 106 (1989), 107-114 Request permission

Abstract:

In this paper, we consider the existence of multiple periodic solutions for the problem \[ \frac {{du}}{{dt}} + Lu = g(u) + h,t > 0,u(0) = u(T),\] where $L$ is a uniformly strongly elliptic operator with domain $D(L) = H_0^m(\Omega ),g:R \to R$ is a continuous mapping, $T > 0$ and $h:(0,T) \to H_0^m(\Omega )$ is a measurable function.

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