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Extremum estimates of the $ L^1 $-norm of weights for eigenvalue problems of vibrating string equations based on critical equations

  • * Corresponding author: Bing Xie

    * Corresponding author: Bing Xie

The first author is supported by the NSF of China grants 11771253, 11971262 and 61977043. The second author is supported by NSF of the Shandong Province grants ZR2019MA038, ZR2019MA050 and ZR2017MA049

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  • The present paper is concerned with the extremal problem of the $ L^1 $-norm of the weights for non-left-definite eigenvalue problems of vibrating string equations with separated boundary conditions. Applying the critical equations of the weights, the infimum is obtained in terms of the given eigenvalue and the parameter in boundary conditions.

    Mathematics Subject Classification: Primary:34B24;Secondary:34L15.


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