Content area
Full Text
http://crossmark.crossref.org/dialog/?doi=10.1007/s10440-014-9961-5&domain=pdf
Web End = Acta Appl Math (2015) 138:153170
DOI 10.1007/s10440-014-9961-5
Yong Huang Zhenhai Liu Stanislaw Migrski
Received: 5 January 2014 / Accepted: 16 July 2014 / Published online: 22 October 2014 Springer Science+Business Media Dordrecht 2014
Abstract This paper is devoted to the existence of solutions for variationalhemivariational inequalities of elliptic type with nonhomogeneous Neumann boundary conditions at resonance as well as at nonresonance. Using the notion of Clarkes generalized gradient and the property of the rst eigenfunction, we also build a Landesman-Lazer theory in the nonsmooth framework of variationalhemivariational inequalities of elliptic type. An application to a static frictional contact problem is provided.
Keywords Boundary elliptic hemivariational inequality Generalized Clarke
subdifferential Pseudomonotone operator Existence of solutions Frictional contact
problem
Mathematics Subject Classication (2000) 35B34 47J20 49J40 65N25
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.
Y. Huang
Department of Mathematics, Baise University, Baise 533000, Guangxi Province, P.R. China e-mail: mailto:[email protected]
Web End [email protected]
Z. Liu (
B)
Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation,and College of Sciences, Guangxi University for Nationalities, Nanning 530006, Guangxi Province, P.R. Chinae-mail: [email protected]
S. Migrski
Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Lojasiewicza 6, 30-348 Krakow, Polande-mail: mailto:[email protected]
Web End [email protected]
Elliptic Hemivariational Inequalitieswith Nonhomogeneous Neumann Boundary Conditions and Their Applications to Static Frictional Contact Problems
154 Y. Huang et al.
1 Introduction
Let
RN be an open bounded domain with a smooth boundary , W1,p() with 1 < p < +, be the usual Sobolev space with the norm u = { |u|p dx + |u|p dx}1/p.
For a convenience, in the following, we denote W1,p() by V . Let A be a mapping from V to its dual space V which is dened by
Au, v V =
xi
and the functions Ai, for i = 0, 1, . . . , N satisfy suitable regularity and growth assumptions
(see below).
Let K be a nonempty, closed and convex...