Open AccessNew fixed point approach for a fully nonlinear fourth order boundary value problem
Author(s) -
Đặng Quang Á,
Ngô Thị Kim Quy
Publication year - 2018
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.v36i4.33584
Subject(s) - uniqueness , mathematics , boundary value problem , nonlinear system , convergence (economics) , fixed point , infinity , reduction (mathematics) , iterative method , initial value problem , iterative and incremental development , function (biology) , order (exchange) , operator (biology) , mathematical analysis , value (mathematics) , mathematical optimization , computer science , software engineering , repressor , economic growth , chemistry , biology , biochemistry , geometry , quantum mechanics , evolutionary biology , transcription factor , physics , finance , economics , gene , statistics
In this paper we propose a method for investigating the solvability and iterative solution of a nonlinear fully fourth order boundary value problem. Namely, by the reduction of the problem to an operator equation for the right-hand side function we establish the existence and uniqueness of a solution and the convergence of an iterative process. Our method completely differs from the methods of other authors and does not require the condition of boundedness or linear growth of the right-hand side function on infinity. Many examples, where exact solutions of the problems are known or not, demonstrate the effectiveness of the obtained theoretical results