Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
Mihai Mihăilescu[1]; Vicenţiu Rădulescu[2]
- [1] University of Craiova Department of Mathematics 200585 Craiova (Romania) Central European University Department of Mathematics 1051 Budapest (Hungary)
- [2] Institute of Mathematics “Simion Stoilow” of the Romanian Academy P.O. Box 1-764 014700 Bucharest (Romania) University of Craiova Department of Mathematics 200585 Craiova (Romania)
Annales de l’institut Fourier (2008)
- Volume: 58, Issue: 6, page 2087-2111
- ISSN: 0373-0956
Access Full Article
topAbstract
topHow to cite
topMihăilescu, Mihai, and Rădulescu, Vicenţiu. "Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces." Annales de l’institut Fourier 58.6 (2008): 2087-2111. <http://eudml.org/doc/10371>.
@article{Mihăilescu2008,
abstract = {We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.},
affiliation = {University of Craiova Department of Mathematics 200585 Craiova (Romania) Central European University Department of Mathematics 1051 Budapest (Hungary); Institute of Mathematics “Simion Stoilow” of the Romanian Academy P.O. Box 1-764 014700 Bucharest (Romania) University of Craiova Department of Mathematics 200585 Craiova (Romania)},
author = {Mihăilescu, Mihai, Rădulescu, Vicenţiu},
journal = {Annales de l’institut Fourier},
keywords = {Nonhomogeneous differential operator; nonlinear partial differential equation; Neumann boundary value problem; Orlicz–Sobolev space; nonhomogeneous differential operator; Orlicz-Sobolev space},
language = {eng},
number = {6},
pages = {2087-2111},
publisher = {Association des Annales de l’institut Fourier},
title = {Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces},
url = {http://eudml.org/doc/10371},
volume = {58},
year = {2008},
}
TY - JOUR
AU - Mihăilescu, Mihai
AU - Rădulescu, Vicenţiu
TI - Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 6
SP - 2087
EP - 2111
AB - We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.
LA - eng
KW - Nonhomogeneous differential operator; nonlinear partial differential equation; Neumann boundary value problem; Orlicz–Sobolev space; nonhomogeneous differential operator; Orlicz-Sobolev space
UR - http://eudml.org/doc/10371
ER -
References
top- Emilio Acerbi, Giuseppe Mingione, Regularity results for a class of functionals with non-standard growth, Arch. Ration. Mech. Anal. 156 (2001), 121-140 Zbl0984.49020MR1814973
- Robert A. Adams, Sobolev spaces, (1975), Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London Zbl0314.46030MR450957
- Haïm Brezis, Analyse fonctionnelle, (1983), Masson, Paris Zbl0511.46001
- Yunmei Chen, Stacey Levine, Murali Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006), 1383-1406 (electronic) Zbl1102.49010MR2246061
- Ph. Clément, M. García-Huidobro, R. Manásevich, K. Schmitt, Mountain pass type solutions for quasilinear elliptic equations, Calc. Var. Partial Differential Equations 11 (2000), 33-62 Zbl0959.35057MR1777463
- Philippe Clément, Ben de Pagter, Guido Sweers, François de Thélin, Existence of solutions to a semilinear elliptic system through Orlicz-Sobolev spaces, Mediterr. J. Math. 1 (2004), 241-267 Zbl1167.35352MR2094464
- Gabriele Dankert, Sobolev Embedding Theorems in Orlicz Spaces, (1966) Zbl0287.46036
- Lars Diening, Theorical and numerical results for electrorheological fluids, (2002) Zbl1022.76001
- Lars Diening, Maximal function on Musielak-Orlicz spaces and generalized Lebesgue spaces, Bull. Sci. Math. 129 (2005), 657-700 Zbl1096.46013MR2166733
- Thomas K. Donaldson, Neil S. Trudinger, Orlicz-Sobolev spaces and imbedding theorems, J. Functional Analysis 8 (1971), 52-75 Zbl0216.15702MR301500
- D. E. Edmunds, J. Lang, A. Nekvinda, On norms, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 455 (1999), 219-225 Zbl0953.46018MR1700499
- David E. Edmunds, Jiří Rákosník, Density of smooth functions in , Proc. Roy. Soc. London Ser. A 437 (1992), 229-236 Zbl0779.46027MR1177754
- David E. Edmunds, Jiří Rákosník, Sobolev embeddings with variable exponent, Studia Math. 143 (2000), 267-293 Zbl0974.46040MR1815935
- I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324-353 Zbl0286.49015MR346619
- Xianling Fan, Jishen Shen, Dun Zhao, Sobolev embedding theorems for spaces , J. Math. Anal. Appl. 262 (2001), 749-760 Zbl0995.46023MR1859337
- Xianling Fan, Dun Zhao, On the spaces and , J. Math. Anal. Appl. 263 (2001), 424-446 Zbl1028.46041MR1866056
- Thomas C. Halsey, Electrorheological Fluids, Science 258 (1992), 761-766
- Ondrej Kováčik, Jiří Rákosník, On spaces and , Czechoslovak Math. J. 41(116) (1991), 592-618 Zbl0784.46029MR1134951
- John Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), 459-466 Zbl0085.09702MR105017
- Paolo Marcellini, Regularity and existence of solutions of elliptic equations with -growth conditions, J. Differential Equations 90 (1991), 1-30 Zbl0724.35043MR1094446
- Mihai Mihăilescu, Patrizia Pucci, Vicenţiu Rădulescu, Nonhomogeneous boundary value problems in anisotropic Sobolev spaces, C. R. Math. Acad. Sci. Paris 345 (2007), 561-566 Zbl1127.35020MR2374465
- Mihai Mihăilescu, Vicenţiu Rădulescu, A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462 (2006), 2625-2641 Zbl1149.76692MR2253555
- Mihai Mihăilescu, Vicenţiu Rădulescu, Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting, J. Math. Anal. Appl. 330 (2007), 416-432 Zbl1176.35071MR2302933
- Mihai Mihăilescu, Vicenţiu Rădulescu, On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent, Proc. Amer. Math. Soc. 135 (2007), 2929-2937 (electronic) Zbl1146.35067MR2317971
- Mihai Mihăilescu, Vicenţiu Rădulescu, Continuous spectrum for a class of nonhomogeneous differential operators, Manuscripta Math. 125 (2008), 157-167 Zbl1138.35070MR2373080
- J. Musielak, W. Orlicz, On modular spaces, Studia Math. 18 (1959), 49-65 Zbl0086.08901MR101487
- Julian Musielak, Orlicz spaces and modular spaces, 1034 (1983), Springer-Verlag, Berlin Zbl0557.46020MR724434
- Hidegorô Nakano, Modulared Semi-Ordered Linear Spaces, (1950), Maruzen Co. Ltd., Tokyo Zbl0041.23401MR38565
- R. O’Neill, Fractional integration in Orlicz spaces, Trans. Amer. Math. Soc. 115 (1965), 300-328 Zbl0132.09201
- Władysław Orlicz, Über konjugierte Exponentenfolgen, Studia Math. 3 (1931), 200-211 Zbl0003.25203
- K. R. Rajagopal, M. Růžička, Mathematical modelling of electrorheological fluids, Cont. Mech. Term. 13 (2001), 59-78 Zbl0971.76100
- M. Růžička, Electrorheological fluids: modeling and mathematical theory, Sūrikaisekikenkyūsho Kōkyūroku (2000), 16-38 Zbl0968.76531MR1788852
- Michael Struwe, Variational methods, 34 (1996), Springer-Verlag, Berlin Zbl0864.49001MR1411681
- V. V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986), 675-710, 877 Zbl0599.49031MR864171
- V. V. Zhikov, Meyer-type estimates for solving the nonlinear Stokes system, Differ. Uravn. 33 (1997), 107-114, 143 Zbl0911.35089MR1607245
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.