کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
839694 | 1470489 | 2014 | 23 صفحه PDF | دانلود رایگان |
The paper proves the existence and uniqueness of the solution for the following multivalued deterministic variational inequality with oblique subgradients, considered in a non-convex domain: {x′(t)+H(t,x(t))∂−φ(x(t))∋g(t,x(t)),t≥0,x(0)=x0, where ∂−φ∂−φ stands for the Fréchet subdifferential of the semiconvex function φφ and the matrix application x↦H(⋅,x)x↦H(⋅,x) is a Lipschitz mapping. The presence of the oblique reflection brought by the term H∂−φH∂−φ leads to the use of different techniques comparing to the cases of standard reflection in non-convex domains or oblique reflection in convex domains. The last section of the article is focused on the qualitative analysis of a non-convex Skorohod problem, with generalized reflection and, as applications, stochastic variational inequalities driven by oblique Fréchet subgradients are addressed.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 111, December 2014, Pages 82–104