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On the semilinear elliptic equations of electrostatic NEMS devices

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Abstract

In this paper, we analyze a class of semilinear elliptic equations with boundary value problem based on electrostatic nanoelectromechanical system. First, we will use upper and lower solution method to study the existence of solutions and some properties of minimal solutions for the problem. Then, we will establish the existence of a second solution by variational method in some conditions.

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Authors and Affiliations

  1. Institute of Contemporary Mathematics, Henan University, Kaifeng, 475004, Henan, People’s Republic of China

    Ruifeng Zhang

  2. School of Mathematics, Henan University, Kaifeng, 475004, Henan, People’s Republic of China

    Ruifeng Zhang

  3. Zhengzhou No. 19 Middle School, Zhengzhou, 450007, Henan, People’s Republic of China

    Liang Cai

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  1. Ruifeng Zhang
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  2. Liang Cai
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Correspondence to Ruifeng Zhang.

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Zhang, R., Cai, L. On the semilinear elliptic equations of electrostatic NEMS devices. Z. Angew. Math. Phys. 65, 1207–1222 (2014). https://doi.org/10.1007/s00033-013-0381-6

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  • DOI: https://doi.org/10.1007/s00033-013-0381-6

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