Science China Mathematics

, Volume 53, Issue 10, pp 2573–2588 | Cite as

Extremal eigenvalues of measure differential equations with fixed variation

  • MeiRong Zhang


In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely continuous. By taking Neumann eigenvalues of measure differential equations as an example, we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth functionals. These results can give another explanation for extremal eigenvalues of Sturm-Liouville operators with integrable potentials.


measure differential equation eigenvalue extremal value weak* topology Frechét derivative sub-differential 


34L15 47N10 58E35 


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© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  2. 2.Zhou Pei-Yuan Center for Applied MathematicsTsinghua UniversityBeijingChina

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