Partial Differential Equations
Nonhomogeneous Neumann problems in Orlicz–Sobolev spaces
Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 401-406.

We establish sufficient conditions for the existence of nontrivial solutions for a class of nonlinear Neumann boundary value problems involving nonhomogeneous differential operators.

On établit des conditions suffisantes pour l'existence des solutions non triviales pour une classe de problèmes aux limites de Neumann avec des opérateurs différentiels non homogènes.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.02.020
Mihăilescu, Mihai 1, 2; Rădulescu, Vicenţiu 1, 3

1 University of Craiova, Department of Mathematics, Street A.I. Cuza No. 13, 200585 Craiova, Romania
2 Department of Mathematics, Central European University, 1051 Budapest, Hungary
3 Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
@article{CRMATH_2008__346_7-8_401_0,
     author = {Mih\u{a}ilescu, Mihai and R\u{a}dulescu, Vicen\c{t}iu},
     title = {Nonhomogeneous {Neumann} problems in {Orlicz{\textendash}Sobolev} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {401--406},
     publisher = {Elsevier},
     volume = {346},
     number = {7-8},
     year = {2008},
     doi = {10.1016/j.crma.2008.02.020},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2008.02.020/}
}
TY  - JOUR
AU  - Mihăilescu, Mihai
AU  - Rădulescu, Vicenţiu
TI  - Nonhomogeneous Neumann problems in Orlicz–Sobolev spaces
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 401
EP  - 406
VL  - 346
IS  - 7-8
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2008.02.020/
DO  - 10.1016/j.crma.2008.02.020
LA  - en
ID  - CRMATH_2008__346_7-8_401_0
ER  - 
%0 Journal Article
%A Mihăilescu, Mihai
%A Rădulescu, Vicenţiu
%T Nonhomogeneous Neumann problems in Orlicz–Sobolev spaces
%J Comptes Rendus. Mathématique
%D 2008
%P 401-406
%V 346
%N 7-8
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2008.02.020/
%R 10.1016/j.crma.2008.02.020
%G en
%F CRMATH_2008__346_7-8_401_0
Mihăilescu, Mihai; Rădulescu, Vicenţiu. Nonhomogeneous Neumann problems in Orlicz–Sobolev spaces. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 401-406. doi : 10.1016/j.crma.2008.02.020. http://www.numdam.org/articles/10.1016/j.crma.2008.02.020/

[1] Chen, Y.; Levine, S.; Rao, M. Variable exponent, linear growth functionals in image processing, SIAM J. Appl. Math., Volume 66 (2006) no. 4, pp. 1383-1406

[2] Diening, L. Maximal function on Musielak–Orlicz spaces and generalized Lebesgue spaces, Bull. Sci. Math., Volume 129 (2005), pp. 657-700

[3] Halsey, T.C. Electrorheological fluids, Science, Volume 258 (1992), pp. 761-766

[4] Mihăilescu, M.; Pucci, P.; Rădulescu, V. Nonhomogeneous boundary value problems in anisotropic Sobolev spaces, C. R. Acad. Sci. Paris, Ser. I, Volume 345 (2007), pp. 561-566

[5] Mihăilescu, M.; Rădulescu, V. A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids, Proc. Roy. Soc. A: Math. Phys. Eng. Sci., Volume 462 (2006), pp. 2625-2641

[6] Mihăilescu, M.; Rădulescu, V. On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent, Proc. Amer. Math. Soc., Volume 135 (2007), pp. 2929-2937

[7] Mihăilescu, M.; Rădulescu, V. Continuous spectrum for a class of nonhomogeneous differential operators, Manuscripta Math., Volume 125 (2008), pp. 157-167

[8] M. Mihăilescu, V. Rădulescu, Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces, Ann. Inst. Fourier, in press

[9] Musielak, J. Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, vol. 1034, Springer, Berlin, 1983

[10] Musielak, J.; Orlicz, W. On modular spaces, Studia Math., Volume 18 (1959), pp. 49-65

[11] Nakano, H. Modulared Semi-ordered Linear Spaces, Maruzen Co., Ltd., Tokyo, 1950

[12] Rajagopal, K.R.; Ružička, M. Mathematical modelling of electrorheological fluids, Cont. Mech. Term., Volume 13 (2001), pp. 59-78

[13] Ružička, M. Electrorheological Fluids Modeling and Mathematical Theory, Springer-Verlag, Berlin, 2002

[14] Struwe, M. Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, Heidelberg, 1996

Cited by Sources: