Monotone iterative technique for nonlinear fourth order integro-differential equations

In this paper, we consider the solvability of a class of nonlinear fourth order integro-differential equations with Navier boundary condition. We first deal with a corresponding linear problem and establish a maximum principle. Using the maximum principle, we develop a monotone iterative technique in the presence of lower and upper solutions to solve the nonlinear problem under certain conditions. Some examples are presented to illustrate the main results.

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