# American Institute of Mathematical Sciences

June  2016, 9(3): 869-893. doi: 10.3934/dcdss.2016033

## On nonlinear and quasiliniear elliptic functional differential equations

 1 Central Economics and Mathematical Institute, Russian Academie of Science, Nakhimovskii pr. 47, Moscow, 117418, Russian Federation

Received  March 2015 Revised  October 2015 Published  April 2016

We consider nonlinear elliptic functional differential equations. The corresponding operator has the form of a product of nonlinear elliptic differential mapping and linear difference mapping. It were obtained sufficient conditions for solvability of the Dirichlet problem. A concrete example shows that a nonlinear differential--difference operator may not be strongly elliptic even if the nonlinear differential operator is strongly elliptic and the linear difference operator is positive definite. The analysis is based on the theory of pseudomonotone--type operators and linear theory of elliptic functional differential operators.
Citation: Olesya V. Solonukha. On nonlinear and quasiliniear elliptic functional differential equations. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 869-893. doi: 10.3934/dcdss.2016033
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