Abstract
J. Y. Park and T. G. Ha [Nonlinear Anal., 2008, 68: 747-767; 2009, 71: 3203-3217] investigated the existence of anti-periodic solutions for hemivariational inequalities with a pseudomonotone operator. In this note, we point out that the methods used there are not suitable for the proof of the existence of anti-periodic solutions for hemivariational inequalities and we shall give a straightforward approach to handle these problems. The main tools in our study are the maximal monotone property of the derivative operator with antiperiodic conditions and the surjectivity result for L-pseudomonotone operators.
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Acknowledgements
The author would like to express his gratitude to the referees for their very valuable comments. This work was supported by the National Natural Science Foundation of China (Grant No. 11501284) and the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 16B224).
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Liu, X. Existence of anti-periodic solutions for hemivariational inequalities. Front. Math. China 13, 607–618 (2018). https://doi.org/10.1007/s11464-018-0699-7
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DOI: https://doi.org/10.1007/s11464-018-0699-7