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Abstract
In this paper, we consider the existence and uniqueness of solutions for the nonlocal elliptic problem
with homogeneous Dirichlet boundary conditions, where ,
. It will be shown that: (i) when
, there exists a unique solution to the nonlocal elliptic problem for any
; (ii) when
, there also exists a unique solution of the nonlocal elliptic problem for
and no solution for
.
Keywords:
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
This work was supported in part by China NSF [grant number 11501442], [grant number 11402194]; Natural Science Foundation of ShaanXi Province [grant number 2016JM1025]; the doctor scientific research start fund project of Xi’an University of Science and Technology [grant number 2016QDJ054]; Engagement Fund project of Xi’an University of Science and Technology [grant number 6310216044].