Chipot, M; Rodrigues, J (1992). On a class of nonlocal nonlinear elliptic problems. RAIRO Modelisation Mathematique et Analyse Numerique, 26(3):447-467.
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We give a direct approach to the solvability of a class of nonlocal problems which admit a formulation in terms of quasi- variational inequalities. We are motivated by nonlinear elliptic boundary value problems in which certain coefficients depend, in a rather general way, on the solution itself through global quantities like the total mass, the total flux or the total energy. We illustrate the existence results with several applications, including an implicit Signorini problem for steady diffusion of biological populations and a class of operator equations in nonlinear mechanics. We also discuss the non- uniqueness of the solutions.
|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Uncontrolled Keywords:||nonlocal problems; quasi-variational inequalities; nonlinear elliptic boundary value problems; existence; Signorini problem; steady diffusion of biological popoluations; nonlinear mechanics; non-uniqueness|
|Deposited On:||31 Aug 2010 08:45|
|Last Modified:||28 Nov 2013 00:30|
|Free access at:||Related URL. An embargo period may apply.|
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