In this paper, we study the linear bond-based nonlocal peridynamic models with a particular focus on problems associated with nonstandard nonlocal displacement loading conditions. Both stationary and time-dependent problems are considered for a one-dimensional scalar equation defined on a finite bar and for a two-dimensional system defined on a square. The related peridynamic operators and asso...

Image nonlocal self-similarity has been widely adopted as natural image prior in various low-level vision tasks such as image restoration, while the low-rank matrix recovery theory has been drawing much attention to describe and utilize the image nonlocal self-similarities. However, whether the low-rank prior models exist to characterize the nonlocal self-similarity for a wide range of natural ...

<p style='text-indent:20px;'>In this paper, a class of nonlocal fractional Dirichlet problems is studied. By using variational principle due to Ricceri (whose original version was given in J. Comput. Appl. Math. 113 (2000), 401–410), the existence infinitely many weak solutions for these established by requiring that nonlinear term <inline-formula><tex-math id="M1">\begin{docu...