Kristály, Alexandru; Varga, Csaba On a class of quasilinear eigenvalue problems in \(\mathbb R^N\). (English) Zbl 1161.35456 Math. Nachr. 278, No. 15, 1756-1765 (2005). Summary: We study an eigenvalue problem in \(\mathbb R^N\) which involves the \(p\)-Laplacian \((p>N\geq 2)\) and the nonlinear term has a global (\(p-1\))-sublinear growth. The existence of certain open intervals of eigenvalues is guaranteed for which the eigenvalue problem has two nonzero, radially symmetric solutions. Some stability properties of solutions with respect to the eigenvalues are also obtained. Cited in 1 ReviewCited in 9 Documents MSC: 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35J60 Nonlinear elliptic equations 47J30 Variational methods involving nonlinear operators Keywords:\(p\)-Laplacian; principle of symmetric criticality; critical points; sublinearity; multiple solutions PDFBibTeX XMLCite \textit{A. Kristály} and \textit{C. Varga}, Math. Nachr. 278, No. 15, 1756--1765 (2005; Zbl 1161.35456) Full Text: DOI References: [1] Multiple nonnegative solutions for elliptic boundary value problems involving the p -Laplacian, preprint. [2] Bartsch, J. Func. Anal. 117 pp 447– (1993) [3] Berestycki, Arch. Ration. Mech. Anal. 82 pp 313– (1983) [4] Bonanno, Nonlinear Anal. 54 pp 651– (2003) [5] Bonanno, J. Global Optim. 28 pp 249– (2004) [6] Bonanno, Arch. Math. Basel 80 pp 424– (2003) [7] Analyse Fonctionnelle-Théorie et Applications (Masson, Paris, 1992). [8] Gazzola, Differential Integral Equations 13 pp 47– (2000) [9] Kristály, Rocky Mountain J. Math. 35 pp 1173– (2005) [10] Kristály, Set-Valued Anal. 13 pp 85– (2005) [11] Li, Comm. Partial Differential Equations 14 pp 1291– (1989) [12] Lions, J. Funct. Anal. 49 pp 315– (1982) [13] Marano, Nonlinear Anal. 48 pp 37– (2002) [14] Montefusco, NoDEA Nonlinear Differential Equations Appl. 8 pp 481– (2001) [15] Palais, Comm. Math. Phys. 69 pp 19– (1979) [16] Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics Vol. 65 (Amer. Math. Soc., Providence, RI, 1986). [17] Ricceri, Arch. Math. Basel 75 pp 220– (2000) [18] Ricceri, Math. Comput. Modelling 32 pp 1485– (2000) [19] Linking Methods in Critical Point Theory (Birkhäuser, Boston, 1999). · Zbl 0915.35001 [20] Schechter, Pacific. J. Math. 214 pp 145– (2004) [21] Strauss, Comm. Math. Phys. 55 pp 149– (1977) [22] Minimax Theorems (Birkhäuser, Boston, 1995). 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.