The thesis proposes a simple but very effective method to study the unique solvability and an iterative method for solving five boundary value problems for nonlinear fourth order ordinary differential equations with different types of boundary conditions and two boundary value problems for a biharmonic equation and a biharmonic equation of Kirchhoff type by using the reduction of these problems to the operator equations for the function to be sought or an intermediate function. | MINISTRY OF EDUCATION VIETNAM ACADEMY OF AND TRAINING SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY ----------------------------------- NGUYEN THANH HUONG SOLVING SOME NONLINEAR BOUNDARY VALUE PROBLEMS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS Major Applied Mathematics Code 9 46 01 12 SUMMARY OF PHD THESIS Hanoi 2019 This thesis has been completed Graduate University of Science and Technology Vietnam Academy of Science and Technology Supervisor 1 Prof. Dr. Dang Quang A Supervisor 2 Dr. Vu Vinh Quang Reviewer 1 Reviewer 2 Reviewer 3 The thesis will be defended at the Board of Examiners of Graduate University of Science and Technology Vietnam Academy of Science and Technology at . on. The thesis can be explored at - Library of Graduate University of Science and Technology - National Library of Vietnam INTRODUCTION 1. Motivation of the thesis Many phenomena in physics mechanics and other fields are modeled by boundary value problems for ordinary differential equations or partial differential equations with different boundary conditions. The qualitative research as well as the method of solving these problems are always the topics attracting the attention of domestic and foreign scientists such as . Agawarl E. Alves P. Amster Z. Bai Y. Li . Ma H. Feng F. Minh os . Wang Dang Quang A Pham Ky Anh Nguyen Dong Anh Nguyen Huu Cong Nguyen Van Dao Le Luong Tai. The existence the uniqueness the positivity of solutions and the iterative method for solving some boundary value problems for fourth order ordinary differential equations or partial differential equations have been considered in the works of Dang Quang A et al. 2006 2010 2016-2018 . Pham Ky Anh 1982 1986 has also some research works on the solvability the structure of solution sets the approximate method of nonlinear periodic boundary value problems. The existence of solutions positive solutions of the beam problems are considered in the works of . Ma 2000 2003 2004 2007 2010 . Theory
