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Equivalence of Fourth Order Boundary Value Problems and Matrix Eigenvalue Problems |
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| Authors: | Ji-jun Ao Jiong Sun Anton Zettl |
| Institution: | 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China 2. College of Sciences, Inner Mongolia University of Technology, Hohhot, 010051, China 3. Mathematics Department, Northern Illinois University, DeKalb, IL, 60115, USA |
| Abstract: | We show that a class of regular self-adjoint fourth order boundary value problems (BVPs) is equivalent to a certain class of matrix problems. Conversely, for any given matrix problem in this class, there exist fourth order self-adjoint BVPs which are equivalent to the given matrix problem. Equivalent here means that they have exactly the same spectrum. |
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