Resolution of semilinear equations by fixed point methods

Semilinear Elliptic Equations and Fixed Points

In this paper, we deal with a class of semilinear elliptic equation in a bounded domain Ω ⊂ R , N ≥ 3, with C boundary. Using a new fixed point result of the Krasnoselskii’s type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.

Multilevel Adaptive Methods for Semilinear Equations

Solving time-fractional chemical engineering equations by modified variational iteration method as fixed point iteration method

The variational iteration method(VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The ob...

Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets

This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving Caputo-Fabrizio fractional derivative without singular kernel admitting only the existence of a lower solution or an upper solution. Our method is based on fixed point in partially ordered sets. In this study, we guaranty the existence of special kind of ...

Optimal Approximate Solutions of Fixed Point Equations

and Applied Analysis 3 Proof. As T and S form a K-Cyclic map, d x1, x2 d Tx0, Sx1 ≤ k d x0, Tx0 d x1, Sx1 1 − 2k d A,B k d x0, x1 d x1, x2 1 − 2k d A,B . 3.1 So, it follows that d x1, x2 ≤ k/ 1 − k d x0, x1 1 − k/ 1 − k d A,B . Similarly, it can be seen that d x2, x3 ≤ ( k 1 − k )2 d x0, x1 [ 1 − ( k 1 − k )2] d A,B . 3.2 Hence, it follows by induction that d xn, xn 1 ≤ ( k 1 − k )n d x0, x1 [ ...