TY - JOUR
T1 - Monotone iterative sequences for non-local elliptic problems
AU - Al-Refai, Mohammed
AU - Kavallaris, Nikos I.
AU - Hajji, Mohamed Ali
PY - 2011/12
Y1 - 2011/12
N2 - In this paper we establish an existence and uniqueness result for a class of non-local elliptic differential equations with the Dirichlet boundary conditions, which, in general, do not accept a maximum principle. We introduce one monotone sequence of lower-upper pairs of solutions and prove uniform convergence of that sequence to the actual solution of the problem, which is the unique solution for some range of γ(the parameter of the problem). The convergence of the iterative sequence is tested through examples with an order of convergence greater than 1.
AB - In this paper we establish an existence and uniqueness result for a class of non-local elliptic differential equations with the Dirichlet boundary conditions, which, in general, do not accept a maximum principle. We introduce one monotone sequence of lower-upper pairs of solutions and prove uniform convergence of that sequence to the actual solution of the problem, which is the unique solution for some range of γ(the parameter of the problem). The convergence of the iterative sequence is tested through examples with an order of convergence greater than 1.
KW - Elliptic Differential Equations
KW - Maximum Principle
KW - Non-Local Problems
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U2 - 10.1017/S0956792511000246
DO - 10.1017/S0956792511000246
M3 - Article
AN - SCOPUS:80055089434
SN - 0956-7925
VL - 22
SP - 533
EP - 552
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
IS - 6
ER -