Nonlinear Sturm-Liouville Theory
In the next chapter, we’ll apply the Krasnoselskii-Rabinowitz bifurcation theorem in a very specific way: to the Euler buckling problem. The buckling problem belongs to an important class of problems in ordinary differential equations called nonlinear Sturm-Liouville problems. To begin this chapter I’ll describe the Euler buckling problem and place it in the more general differential equation context. Then I’ll apply the bifurcation theorem to the general class of nonlinear Sturm-Liouville problems, to obtain a tool that I’ll be able to use in the next chapter for the buckling problem.
KeywordsBounded Subset Fixed Point Problem Bifurcation Theorem Separate Boundary Condition Buckle Column
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