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Calderon-Type Uniqueness Theorem for Stochastic Partial Differential Equations
In this Note, we present a Calder\'on-type uniqueness theorem on the Cauchy
problem of stochastic partial differential equations. To this aim, we introduce
the concept of stochastic pseudo-differential operators, and establish their
boundedness and other fundamental properties. The proof of our uniqueness
theorem is based on a new Carleman-type estimate.Comment:
Multibump solutions of a class of second-order discrete Hamiltonian systems
For a class of second-order discrete Hamiltonian systems
, we investigate the existence of
homoclinic orbits by applying variational method, where and
are periodic functions. Further, we show that there exist either uncountable
many homoclinic orbits or multibump solutions under certain conditions
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