zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Existence results for quasilinear parabolic hemivariational inequalities. (English) Zbl 1139.35006
In this paper it is studied a class of parabolic hemivariational inequalities involving pseudomonotone operators. The main result of the paper establishes the existence of a nontrivial solution. Connections with the Landesman-Lazer resonance theory are also made in the present paper. The proofs rely on monotonicity arguments combined with the Clarke critical point theory for locally Lipschitz functionals.
35A15Variational methods (PDE)
35K85Linear parabolic unilateral problems; linear parabolic variational inequalities
49J40Variational methods including variational inequalities
[1]Ahmad, S.; Lazer, A. C.; Paul, J. L.: Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana univ. Math. J. 25, 933-944 (1976) · Zbl 0351.35036 · doi:10.1512/iumj.1976.25.25074
[2]Aizicovici, S.; Papageorgiou, N. S.; Staicu, V.: Periodic solutions of nonlinear evolution inclusions in Banach spaces, J. nonlinear convex anal. 7, No. 2, 163-177 (2006) · Zbl 1110.34037
[3]Carl, S.; Motreanu, D.: Extremal solutions of quasilinear parabolic inclusions with generalized clarke’s gradient, J. differential equations 191, 206-233 (2003) · Zbl 1042.35092 · doi:10.1016/S0022-0396(03)00022-6
[4]Chang, K. C.: Variational methods for nondifferentiable functionals and their applications to partial differential equations, J. math. Anal. appl. 80, 102-129 (1981) · Zbl 0487.49027 · doi:10.1016/0022-247X(81)90095-0
[5]Clarke, F. H.: Optimization and nonsmooth analysis, (1990)
[6]Denkowski, Z.; Migorski, S.: A system of evolution hemivariational inequalities modeling thermoviscoelastic frictional contact, Nonlinear anal. 60, No. 8, 1415-1441 (2005) · Zbl 1190.74019 · doi:10.1016/j.na.2004.11.004
[7]Denkowski, Z.; Migorski, S.; Papageorgiou, N. S.: An introduction to nonlinear analysis: applications, (2003)
[8]Goeleven, D.; Motreanu, D.; Panagiotopoulos, P. D.: Eigenvalue problems for variational – hemivariational inequalities at resonance, Nonlinear anal. 33, No. 2, 161-180 (1998) · Zbl 0939.74021 · doi:10.1016/S0362-546X(97)00521-X
[9]Hess, P.: On a theorem of landesman and lazer, Indiana univ. Math. J. 23, 827-829 (1974) · Zbl 0259.35036 · doi:10.1512/iumj.1974.23.23068
[10]Landesman, E. M.; Lazer, A. C.: Nonlinear perturbations of linear elliptic boundary value problems, J. math. Mech. 7, 609-623 (1970) · Zbl 0193.39203
[11]Zhenhai Liu, On eigenvalue problems for elliptic hemivariational inequalities, Proc. Edinb. Math. Soc., in press · Zbl 1151.35311 · doi:10.1017/S0013091506001246
[12]Liu, Zhenhai: Browder – Tikhonov regularization of non-coercive evolution hemivariational inequalities, Inverse problems 21, No. 1, 13-20 (2005) · Zbl 1078.49006 · doi:10.1088/0266-5611/21/1/002
[13]Liu, Zhenhai: A class of evolution hemivariational inequalities, Nonlinear anal. 36, 91-100 (1999) · Zbl 0920.47056 · doi:10.1016/S0362-546X(98)00016-9
[14]Liu, Zhenhai: On doubly degenerate quasilinear parabolic equations of higher order, Acta math. Sin. (Engl. Ser.) 21, No. 1, 197-208 (2005) · Zbl 1084.35036 · doi:10.1007/s10114-004-0415-2
[15]Liu, Zhenhai: On quasilinear elliptic hemivariational inequalities, Appl. math. Mech. 20, No. 2, 225-230 (1999) · Zbl 0932.49010 · doi:10.1007/BF02481903
[16]Liu, Zhenhai; Zhang, Shisheng: On the degree theory for multivalued (S+) type mappings, Appl. math. Mech. 19, 1141-1149 (1998) · Zbl 0941.47051 · doi:10.1007/BF02456635
[17]Migorski, S.; Ochal, A.: Existence of solutions for second order evolution inclusions with application to mechanical contact problems, Optimization 55, No. 1 – 2, 101-120 (2006) · Zbl 1104.34045 · doi:10.1080/02331930500530187
[18]Ye, Q. X.; Li, Z. Y.: Introduction to reaction – diffusion equations, (1990) · Zbl 0774.35037
[19]Zeidler, E.: Nonlinear functional analysis and its applications, IIA and IIB, (1990)