Extremal Eigenvalues for a Sturm-Liouville Problem
نویسنده
چکیده
We consider the fourth order boundary value problem (ry′′)′′+(py′)′+ qy = λwy, y(a) = y′(a) = y(b) = y′(b) = 0, which is used in a variety of physical models. For such models, the extremal values of the smallest eigenvalue help answer certain optimization problems, such as maximizing the fundamental frequency of a vibrating elastic system or finding the tallest column that will not buckle under its own weight. We prove the existence of coefficient functions that correspond to the extremal values of the smallest eigenvalue, while allowing the coefficients to vary over a particular class of L1 functions. However, these extremizing functions do not necessarily belong to the same class of functions. Mathematics Subject Classification: 34B09, 34B24
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