A novel approach to fully third order nonlinear boundary value problems
Provides a more efficient theoretical framework for analyzing third-order BVPs, but the contribution is incremental as it extends existing operator-based methods to a specific class of problems.
The authors propose a new approach for solving fully third-order nonlinear boundary value problems by reducing them to operator equations for the nonlinear terms, establishing existence, uniqueness, positivity, and monotonicity of solutions under simpler and weaker conditions than previous methods.
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the functions to be sought. By this approach we have established the existence, uniqueness, positivity and monotony of solutions and the convergence of the iterative method for approximating the solutions under some easily verified conditions in bounded domains. These conditions are much simpler and weaker than those of other authors for studying solvability of the problems before by using different methods. Many examples illustrate the obtained theoretical results.