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Elliptic Hemivariational Inequalities with Nonhomogeneous Neumann Boundary Conditions and Their Applications to Static Frictional Contact Problems

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Abstract

This paper is devoted to the existence of solutions for variational–hemivariational inequalities of elliptic type with nonhomogeneous Neumann boundary conditions at resonance as well as at nonresonance. Using the notion of Clarke’s generalized gradient and the property of the first eigenfunction, we also build a Landesman-Lazer theory in the nonsmooth framework of variational–hemivariational inequalities of elliptic type. An application to a static frictional contact problem is provided.

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Authors and Affiliations

  1. Department of Mathematics, Baise University, Baise, 533000, Guangxi Province, P.R. China

    Yong Huang

  2. Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, and College of Sciences, Guangxi University for Nationalities, Nanning, 530006, Guangxi Province, P.R. China

    Zhenhai Liu

  3. Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Lojasiewicza 6, 30-348, Krakow, Poland

    Stanislaw Migórski

Authors
  1. Yong Huang
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  2. Zhenhai Liu
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  3. Stanislaw Migórski
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Correspondence to Zhenhai Liu.

Additional information

Project supported by NNSF of China Grants Nos. 11271087, 61263006, NSF of Guangxi Grant No. 2013GXNSFAA019022. The research was also supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118 and the National Science Center of Poland under Maestro Advanced Project No. UMO-2012/06/A/ST1/00262.

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Huang, Y., Liu, Z. & Migórski, S. Elliptic Hemivariational Inequalities with Nonhomogeneous Neumann Boundary Conditions and Their Applications to Static Frictional Contact Problems. Acta Appl Math 138, 153–170 (2015). https://doi.org/10.1007/s10440-014-9961-5

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  • DOI: https://doi.org/10.1007/s10440-014-9961-5

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