ON THE EXISTENCE OF ANTIPERIODIC SOLUTIONS TO A NONLINEAR EVOLUTION EQUATION ASSOCIATED WITH ODD SUBDIFFERENTIAL OPERATORS
ON THE EXISTENCE OF ANTIPERIODIC SOLUTIONS TO A NONLINEAR EVOLUTION EQUATION ASSOCIATED WITH ODD SUBDIFFERENTIAL OPERATORS
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DOI：
10.1016/0022-1236(90)90143-9
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发表时间：
1990-07-01
影响因子：
1.7
通讯作者：
OKOCHI, H
中科院分区：
文献类型：
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作者：
OKOCHI, H
在次微分算子是奇的和{+ F（t）; t∈ R}是满足反周期条件F（t+T）（− v）-− F（t）v，v∈ D（F（t））的单调算子族（因此，{+ F（t+T）}（− v）=−{+ F（t）} v，v∈ D（）<$D（F（t），T∈：R，对于固定的T∈：R。这里没有假设不确定性。在不假定R × n的区域有界的情况下，给出了一个热方程的应用.
The existence of anti-periodic solutions, hence also that of periodic solutions, to the nonlinear parabolic-type evolution equation (d dt) u (t)+∂ ϑ (u (t))+ F (t) u (t)∋ 0, t∈ R is shown under the assumptions that the subdifferential operator∂ ϑ is odd and that {∂ ϑ+ F (t); t∈ R} is a family of monotone operators satisfying the anti-periodicity condition F (t+T)(− v)-− F (t) v, v∈ D (F (t))(hence,{∂ ϑ+ F (t+T)}(− v)=−{∂ ϑ+ F (t)} v, v∈ D (∂ ϑ)∩ D (F (t))), T∈: R, for a fixed T∈: R. Here coerciveness of∂ ϑ is not assumed. An application to a heat equation is given without assuming boundedness of the domain of R x n.