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In this paper, we study the nonlocal dispersal equation{ut=∫RNJ(x−y)u(y,t)dy−u+λu−a(x,t)up in Ω¯×(0,+∞),u(x,t)=0 in (RN∖Ω¯)×(0,+∞),u(x,0)=u0(x) in Ω¯, where Ω⊂RN is a bounded domain, λ and p>1 are constants. The dispersal kernel J is nonnegative. The function a∈C(Ω¯×R) is nonnegative and T-periodic in t, but a(x,t) has temporal or spatial degeneracies (a(x,t) vanishes). We first study the periodic...
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