| [1] Cl\'{e}ment P, Pagter B, Sweers G, Th\'{e}lin F. Existence of solutions to a semilinear elliptic system through Orlicz-Sobolev spaces, Mediterranean Journal of Mathematics, 2004, 1: 241--267
[2] Krasnosel'skii M A, Rutickii Ya B. Convex Functions and Orlicz Spaces. Gr\"{o}ningen: Noordhoff, 1961
[3] Rao M M, Ren Z D.Theory of Orlicz Spaces. New York: Marcel Dekker, 1991
[4] Luxemberg W. Banach Function Spaces [D]. Technische Hogeschool te Delft, The Netherland: Delft Tech Univ, 1955
[5] Adams R. Sobolev Spaces. New York: Academic Press, 1975
[6] Donaldson T. Nonlinear elliptic boundary value problems in Orlicz-Sobolev spaces. J Differential Equations, 1971, 10: 507--528
[7] Gossez J. Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients. Trans Amer Math Soc, 1974, 190: 163--205
[8] Gossez J. A strongly nonlinear elliptic problem in Orlicz-Sobolev space. Proc Symp Pure Math, 1986, 45: 455--462
[9] Cl\'{e}ment Ph, Garc\'{\i}a-Huidobro M, Man\'{a}sevich R, Schmitt K. Mountain pass type solutions for quasilinear elliptic equations. Calc Var, 2000, 11: 33--62
[10] Fukagai N, Ito M, Narukawa K. Positive solutions of quasilinear elliptic equations with critical Orlicz-Sobolev nonlinearity on RN. Funkcialaj Ekvacioj, 2006, 49: 235--267
[11] Fukagai N, Narukawa K. On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems. Annali di Matematica, 2007, 186: 539--564
[12] Garc\'{\i}a-Huidobro M, Le V K, Man\'{a}sevich R, Schmitt K. On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting. Nonlinear Differential Equations Appl, 1999, 6: 207--225
[13] Mih\u{a}ilescu M, R\u{a}dulescu V. Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting. J Math Anal Appl, 2007, 330: 416--432
[14] Ambrosetti A, Br\'{e}zis H, Cerami G. Combined effects of concave and convex nonlinearities in some elliptic problems. J Funct Anal, 1994, 122: 519--543
[15] Bartsch T, Willem M. On an elliptic equation with concave and convex nonlinearities. Proc Amer Math Soc, 1995, 123: 3555--3561
[16] Rabinowitz P H. Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS Reg Conf Ser Math 65. Providence, RI: Amer Math Soc, 1986
[17] Willem M. Minimax Theorems, Progress in Nonlinear Differential Equations and Their Applications. Boston: Birkhauser, 1996
[18] Clark D C. A variant of the Ljusternik-Schnirelmann theory. Indiana Univ Math J, 1972, 22: 65--74
[19] Heinz H.P. Free Ljusternik-Schnirelmann theory and the bifurcation diagrams of certain singular nonlinear systems. J Differential Equations, 1987, 66: 263--300 |