Investigation in Nonlinear Mechanics.
Final rept. 16 Sep 73-15 Sep 77,
MINNESOTA UNIV MINNEAPOLIS
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The first phase of this work was the completion of the project on stability regions for Hills equation. The main result was a description of the asymptotic behavior of the stability regions for large values of the parameters in the equation. Equations for asymptotic curves for the stability boundaries were obtained in a number of cases. The principal thrust of the work on this project has been the study of branching phenomena associated with general boundary-value problems for ordinary differential equations. The problem considered has been 1 x Ft,x,mu Axa Bxb k where it is further assumed that there is a solution x sub 0t of the problem when mu 0. Results have included a qualitative description of the simpler cases of branching for both the vector case and the scalar case. A further phase of the project has had to do with the group inverse of a differential operator and its application to branching problems for nonlinear systems. Author
- Numerical Mathematics