Boureanu, Maria-Magdalena; Pucci, Patrizia; Rădulescu, Vicenţiu D. Multiplicity of solutions for a class of anisotropic elliptic equations with variable exponent. (English) Zbl 1229.35086 Complex Var. Elliptic Equ. 56, No. 7-9, 755-767 (2011). The authors study quasilinear elliptic equations involving the anisotropic \(p(x)\)-Laplace operator on a bounded domain with smooth boundary. Using the symmetric mountain pass theorem of Ambrosetti and Rabinowitz they obtain the existence of an unbounded sequence of solutions. Reviewer: Leszek Gasiński (Kraków) Cited in 1 ReviewCited in 19 Documents MSC: 35J62 Quasilinear elliptic equations 35J25 Boundary value problems for second-order elliptic equations 35D30 Weak solutions to PDEs 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 35J20 Variational methods for second-order elliptic equations Keywords:quasilinear elliptic equations; multiple weak solutions; anisotropic variable exponent; Sobolev spaces; symmetric mountain pass theorem PDFBibTeX XMLCite \textit{M.-M. Boureanu} et al., Complex Var. Elliptic Equ. 56, No. 7--9, 755--767 (2011; Zbl 1229.35086) Full Text: DOI References: [1] DOI: 10.1070/RM1961v016n05ABEH004113 · Zbl 0117.29101 · doi:10.1070/RM1961v016n05ABEH004113 [2] Rákosník J, Beiträge zur Anal. 13 pp 55– (1979) [3] Rákosník J, Beiträge zur Anal. 15 pp 127– (1981) [4] Troisi M, Ric. Mat. 18 pp 3– (1969) [5] Ven’–tuan L, Vestn. Leningrad Univ. 16 pp 23– (1961) [6] DOI: 10.1098/rspa.1999.0309 · Zbl 0953.46018 · doi:10.1098/rspa.1999.0309 [7] DOI: 10.1098/rspa.1992.0059 · Zbl 0779.46027 · doi:10.1098/rspa.1992.0059 [8] Edmunds DE, Stud. Math. 143 pp 267– (2000) [9] Kováčik O, Czechoslovak Math. J. 41 pp 592– (1991) [10] DOI: 10.1098/rspa.2005.1633 · Zbl 1149.76692 · doi:10.1098/rspa.2005.1633 [11] DOI: 10.1090/S0002-9939-07-08815-6 · Zbl 1146.35067 · doi:10.1090/S0002-9939-07-08815-6 [12] Musielak J, Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics 1034 (1983) · Zbl 0557.46020 · doi:10.1007/BFb0072210 [13] DOI: 10.1016/j.jmaa.2005.02.002 · Zbl 1079.47053 · doi:10.1016/j.jmaa.2005.02.002 [14] DOI: 10.1063/1.1698285 · doi:10.1063/1.1698285 [15] DOI: 10.1515/crll.2005.2005.584.117 · Zbl 1093.76003 · doi:10.1515/crll.2005.2005.584.117 [16] DOI: 10.1016/j.jmaa.2004.10.028 · Zbl 1160.35399 · doi:10.1016/j.jmaa.2004.10.028 [17] DOI: 10.1016/j.jmaa.2005.03.057 · Zbl 1154.35336 · doi:10.1016/j.jmaa.2005.03.057 [18] DOI: 10.1016/j.jmaa.2003.11.020 · Zbl 1072.35138 · doi:10.1016/j.jmaa.2003.11.020 [19] DOI: 10.1126/science.258.5083.761 · doi:10.1126/science.258.5083.761 [20] Pfeiffer, C, Mavroidis, C, Bar-Cohen, Y and Dolgin, B. 1999.Electrorheological fluid based force feedback device, Proceeding of the 1999 SPIE Telemanipulator and Telepresence Technologies VI ConferenceVol. 3840, 88–99. Boston, MA [21] DOI: 10.1007/s001610100034 · Zbl 0971.76100 · doi:10.1007/s001610100034 [22] Rüžička M, Electrorheological Fluids: Modeling and Mathematical Theory (2002) [23] DOI: 10.1070/IM1987v029n01ABEH000958 · Zbl 0599.49031 · doi:10.1070/IM1987v029n01ABEH000958 [24] Mihăilescu M, C. R. Acad. Sci. Paris, Ser. I 345 pp 561– (2007) · Zbl 1127.35020 · doi:10.1016/j.crma.2007.10.012 [25] DOI: 10.1016/j.jmaa.2007.09.015 · Zbl 1135.35058 · doi:10.1016/j.jmaa.2007.09.015 [26] DOI: 10.1016/j.anihpc.2003.12.001 · Zbl 1144.35378 · doi:10.1016/j.anihpc.2003.12.001 [27] Antontsev S, J. Math. Anal. Appl. 361 pp 371– (2010) · Zbl 1183.35177 · doi:10.1016/j.jmaa.2009.07.019 [28] Boureanu M-M, Adv. Pure Appl. Math. 1 pp 387– (2010) · Zbl 1198.35103 · doi:10.1515/apam.2010.025 [29] Ji C, Nonlinear Analysis TMA 71 pp 4507– (2009) · Zbl 1177.35074 · doi:10.1016/j.na.2009.03.020 [30] Kone B, Electron. J. Differ. Equ. 2009 pp 1– (2009) [31] DOI: 10.1080/00036810802713826 · Zbl 1187.35074 · doi:10.1080/00036810802713826 [32] DOI: 10.1016/0022-1236(73)90051-7 · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7 [33] Jabri Y, The Mountain Pass Theorem: Variants, Generalizations and some Applications (2003) · Zbl 1036.49001 · doi:10.1017/CBO9780511546655 [34] Harjulehto P, Math. Bohem. 132 pp 125– (2007) [35] Hästö P, Rev. Mat. Iberoam. 23 pp 74– (2007) [36] DOI: 10.1007/s11118-006-9023-3 · Zbl 1120.46016 · doi:10.1007/s11118-006-9023-3 [37] DOI: 10.1016/j.na.2010.02.033 · Zbl 1188.35072 · doi:10.1016/j.na.2010.02.033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.