Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: An Orlicz-Sobolev space setting

Journal of Mathematical Analysis and Applications

Volumn 330, Issue 1, 2007, Pages 416-432

  Mihǎilescu, Mihai ^a   Rǎdulescu, Vicenţiu ^a  

^a UNIVERSITY OF CRAIOVA   (Romania)

Author keywords

Critical point; Nonhomogeneous operator; Orlicz Sobolev space; Weak solution

Indexed keywords

EID: 33846913726     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.07.082     Document Type: Article

References (26)

1. Acerbi E., and Mingione G. Gradient estimates for the p (x)-Laplacean system. J. Reine Angew. Math. 584 (2005) 117-148
2. Adams R. Sobolev Spaces (1975), Academic Press, New York
3. Ambrosetti A., and Rabinowitz P.H. Dual variational methods in critical point theory and applications. J. Funct. Anal. 14 (1973) 349-381
4. Benci V., and Fortunato D. Discreteness conditions of the spectrum of Schrödinger operators. J. Math. Anal. Appl. 64 (1978) 695-700
5. Chabrowski J., and Fu Y. Existence of solutions for p (x)-Laplacian problems on a bounded domain. J. Math. Anal. Appl. 306 (2005) 604-618
6. Chen Y., Levine S., and Rao R. Functionals with p (x)-growth in image processing. Duquesne University, Department of Mathematics and Computer Science Technical Report 2004-01, available at. http://www.mathcs.duq.edu/~sel/CLR05SIAPfinal.pdf
7. Clément Ph., García-Huidobro M., Manásevich R., and Schmitt K. Mountain pass type solutions for quasilinear elliptic equations. Calc. Var. 11 (2000) 33-62
8. Clément Ph., de Pagter B., Sweers G., and de Thélin F. Existence of solutions to a semilinear elliptic system through Orlicz-Sobolev spaces. Mediterr. J. Math. 1 (2004) 241-267
9. G. Dankert, Sobolev embedding theorems in Orlicz spaces, PhD thesis, University of Köln, 1966
10. Donaldson T.K. Nonlinear elliptic boundary value problems in Orlicz-Sobolev spaces. J. Differential Equations 10 (1971) 507-528
11. Donaldson T.K., and Trudinger N.S. Orlicz-Sobolev spaces and imbedding theorems. J. Funct. Anal. 8 (1971) 52-75
12. Fan X. Solutions for p (x)-Laplacian Dirichlet problems with singular coefficients. J. Math. Anal. Appl. 312 (2005) 464-477
13. Fan X., Zhang Q., and Zhao D. Eigenvalues of p (x)-Laplacian Dirichlet problem. J. Math. Anal. Appl. 302 (2005) 306-317
14. García-Huidobro M., Le V.K., Manásevich R., and Schmitt K. On principal eigenvalues for quasilinear elliptic differential operators: An Orlicz-Sobolev space setting. Nonlinear Differential Equations Appl. 6 (1999) 207-225
15. Gossez J.P. Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients. Trans. Amer. Math. Soc. 190 (1974) 163-205
16. Gossez J.P. A strongly nonlinear elliptic problem in Orlicz-Sobolev spaces. Proc. Sympos. Pure Math. vol. 45 (1986), Amer. Math. Soc., Providence, RI 455-462
17. Le V.K., and Schmitt K. Quasilinear elliptic equations and inequalities with rapidly growing coefficients. J. London Math. Soc. 62 (2000) 852-872
18. W. Luxemburg, Banach function spaces, PhD thesis, Technische Hogeschool te Delft, The Netherlands, 1955
19. Krasnosel'skii M.A., and Rutickii Ya.B. Convex Functions and Orlicz Spaces (1961), Noordhoff, Gröningen
20. Kufner A., John O., and Fučik S. Function Spaces (1997), Noordhoff, Leyden
21. Mihǎilescu M., and Rǎdulescu V. A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids. Proc. Roy. Soc. London Ser. A 462 (2006) 2625-2641
22. O'Neill R. Fractional integration in Orlicz spaces. Trans. Amer. Math. Soc. 115 (1965) 300-328
23. Rabinowitz P. Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS Reg. Conf. Ser. Math. (1984), Amer. Math. Soc., Providence, RI
24. Reed M., and Simon B. Methods of Modern Mathematical Physics, vol. IV, Analysis of Operators (1978), Academic Press, New York
25. Ružička M. Electrorheological Fluids: Modeling and Mathematical Theory (2000), Springer, Berlin
26. Struwe M. Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (1996), Springer, Heidelberg