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A Fixed Point Theorem for Systems of Nonlinear Operator Equations and Applications to \((p_1, p_2)\)-Laplacian System

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Abstract

A new fixed point theorem for systems of nonlinear operator equations is established by means of topological degree theory and positively 1-homogeneous operator, where the components has a positively 1-homogeneous majorant or minorant. As applications, the existence of positive solutions for \((p_1, p_2)\)-Laplacian system is considered under some conditions concerning the positive eigenvalues corresponding to the relevant positively 1-homogeneous operators.

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Acknowledgements

The Project Supported by the National Natural Science Foundation of China (11371221) and Shandong Natural Science Foundation (ZR2018MA011).

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Authors and Affiliations

  1. Department of Statistics and Finance, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    Yumei Zou

  2. Shandong Academy of Sciences, Jinan, 250014, People’s Republic of China

    Guoping He

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  1. Yumei Zou
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  2. Guoping He
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Correspondence to Yumei Zou.

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Zou, Y., He, G. A Fixed Point Theorem for Systems of Nonlinear Operator Equations and Applications to \((p_1, p_2)\)-Laplacian System. Mediterr. J. Math. 15, 74 (2018). https://doi.org/10.1007/s00009-018-1119-7

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  • DOI: https://doi.org/10.1007/s00009-018-1119-7

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