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On the optimization problems of the principal eigenvalues of measure differential equations with indefinite measures

  • * Corresponding author: Zhiyuan Wen

    * Corresponding author: Zhiyuan Wen 

The first author is supported the Scientific Starting Research Foundation of Inner Mongolia University (No. 21200-5175108) and the National Natural Science Foundation of China (No. 11901321). The second author is supported by the National Natural Science Foundation of China (No. 11790273)

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  • In this paper, we will first establish the necessary and sufficient conditions for the existence of the principal eigenvalues of second-order measure differential equations with indefinite weighted measures subject to the Neumann boundary condition. Then we will show the principal eigenvalues are continuously dependent on the weighted measures when the weak$^*$ topology is considered for measures. As applications, we will finally solve several optimization problems on principal eigenvalues, including some isospectral problems.

    Mathematics Subject Classification: Primary: 34L05, 34L15; Secondary: 49K15, 58J53.


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