Multipoint initial-final value problems for dynamical Sobolev-type equations in the space of noises. (English) Zbl 1434.60139

Summary: We prove the existence of a unique solution for a linear stochastic Sobolev-type equation with a relatively \(p\)-bounded operator and a multipoint initial-final condition, in the space of “noises”. We apply the abstract results to specific multipoint initial-final and boundary value problems for the linear Hoff equation which models I-beam bulging under random load.


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K50 Stochastic functional-differential equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H40 White noise theory
47A10 Spectrum, resolvent
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