Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone...

Abstrac-Based on a variational principle, a new approach to derive the exact boundary equation for the analysis of nonlinear Reissner plates and a related existing criterion for the solution of the boundary integral equation is presented in this paper. In this procedure, the boundary and the domain of the plate are discredited to solve the nonlinear problems. All unknown variables are at the bo...

We propose and analyze a numerical method for solving the nonlinear Poisson equation −Δu = f(·, u) on the unit disk with zero Dirichlet boundary conditions. The problem is reformulated as a nonlinear integral equation. We use a Galerkin method with polynomials as approximations. The speed of convergence is shown to be very rapid; and experimentally the maximum error is exponentially decreasing ...