حلول التفرع ذات ثلاث انماط لبعض المعادلات التفاضلية غير الخطية من الرتبة الرابعة == Three - Modes Bifurcation Solutions of Some Nonlinear Fourth Order Differential Equations
Author name:
احمد كاظم شنان الجابري
Supervisor name:
مظهر عبد الواحد عبد الحسين
General topic:
Mathematics
Specific topic:
Differential Equations
Degree:
Master
University:
University Of Basrah - Faculty Of Education
Language:
Arabic
University location:
Basrah
First pages:
27T1091 - p.pdf
Abstract:
This thesis, is interested in the study of bifurcation solutions of some nonlinear fourth order differential equations by using the local method of Lyapunov - Schmidt. Two ways have been used in this study, the first is by using the general local method of Lyapunov - Schmidt and the second is by using the local method of Lyapunov - Schmidt in the variational case. In the first way we found bifurcation solutions of boundary value problem, It is showed that the bifurcation equation corresponding to the above boundary value problem is given by a nonlinear system of three equations. Also, we found the bifurcation diagram of the specifial problem. In the second we studied bifurcation solutions of boundary value of the equation, in the variational case, dxhe normal form of the key function corresponding to the functional, has been found. Also, we found a new geometrical description of Caustic with the bifurcation spreading of the critical points.
