Comparison estimates on the first eigenvalue of a quasilinear elliptic system

References

[1] A. Abolarinwa, The first eigenvalue of p-Laplacian and geometric estimates, J. Nonlinear Anal. Differ. Equ. 2 (2014), no. 3, 105–115. 10.12988/nade.2014.455Suche in Google Scholar

[2] A. Abolarinwa, Evolution and monotonicity of the first eigenvalue of p-Laplacian under the Ricci-harmonic flow, J. Appl. Anal. 21 (2015), no. 2, 147–160. 10.1515/jaa-2015-0013Suche in Google Scholar

[3] A. Abolarinwa, Eigenvalues of the weighted Laplacian under the extended Ricci flow, Adv. Geom. 19 (2019), no. 1, 131–143. 10.1515/advgeom-2018-0022Suche in Google Scholar

[4] A. Abolarinwa, O. Adebimpe and E. A. Bakare, Monotonicity formulas for the first eigenvalue of the weighted p-Laplacian under the Ricci-harmonic flow, J. Inequal. Appl. 2019 (2019), Paper No. 10. 10.1186/s13660-019-1961-6Suche in Google Scholar

[5] A. Abolarinwa, S. O. Edeki and J. O. Ehigie, On the spectrum of the weighted p-Laplacian under the Ricci-harmonic flow, J. Inequal. Appl. 2020 (2020), Paper No. 58. 10.1186/s13660-020-02322-ySuche in Google Scholar

[6] A. Abolarinwa, C. Yang and D. Zhang, On the spectrum of the p-biharmonic operator under the Ricci flow, Results Math. 75 (2020), no. 2, Paper No. 54. 10.1007/s00025-020-1182-9Suche in Google Scholar

[7] G. A. Afrouzi, M. Mirzapour and Q. Zhang, Simplicity and stability of the first eigenvalue of a (p;q) Laplacian system, Electron. J. Differential Equations 2012 (2012), Paper No. 08. Suche in Google Scholar

[8] T. Aubin, Some Nonlinear Problems in Riemannian Geometry, Springer Monogr. Math., Springer, Berlin, 1998. 10.1007/978-3-662-13006-3Suche in Google Scholar

[9] S. Azami, The first eigenvalue of some (p,g)-Laplacian and geometric estimates, Commun. Korean Math. Soc. 33 (2018), no. 1, 317–323. Suche in Google Scholar

[10] C. Bennett and R. Sharpley, Interpolation of Operators, Pure Appl. Math. 129, Academic Press, Boston, 1988. Suche in Google Scholar

[11] N. Benouhiba and Z. Belyacine, A class of eigenvalue problems for the (p,q)-Laplacian in ℝN, Int. J. Pure Appl. Math. 80 (2012), no. 5, 727–737. Suche in Google Scholar

[12] B. Benson, The Cheeger constant, isoperimetric problems, and hyperbolic surfaces, preprint (2015), https://arxiv.org/abs/1509.08993. Suche in Google Scholar

[13] P. Bérard and D. Meyer, Inégalités isopérimétriques et applications, Ann. Sci. Éc. Norm. Supér. (4) 15 (1982), no. 3, 513–541. 10.24033/asens.1435Suche in Google Scholar

[14] J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Problems in Analysis, Princeton University, Princetom (1970), 195–199. 10.1515/9781400869312-013Suche in Google Scholar

[15] S. Y. Cheng, Eigenfunctions and eigenvalues of Laplacian, Differential Geometry, Proc. Sympos. Pure Math. Part 2 27, Stanford University, Stanford (1975), 185–193. 10.1090/pspum/027.2/0378003Suche in Google Scholar

[16] S. Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), no. 3, 289–297. 10.1007/BF01214381Suche in Google Scholar

[17] P. L. De Nápoli and J. P. Pinasco, Estimates for eigenvalues of quasilinear elliptic systems, J. Differential Equations 227 (2006), no. 1, 102–115. 10.1016/j.jde.2006.01.004Suche in Google Scholar

[18] A. El Khalil, S. El Manouni and M. Ouanan, Simplicity and stability of the first eigenvalue of a nonlinear elliptic system, Int. J. Math. Math. Sci. 205 (2005), no. 10, 1555–1563. 10.1155/IJMMS.2005.1555Suche in Google Scholar

[19] J. Fernández Bonder and J. P. Pinasco, Estimates for eigenvalues of quasilinear elliptic systems. II, J. Differential Equations 245 (2008), no. 4, 875–891. 10.1016/j.jde.2008.04.019Suche in Google Scholar

[20] J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis and F. de Thélin, Principal eigenvalues for some quasilinear elliptic equations on 𝐑N, Adv. Differential Equations 2 (1997), no. 6, 981–1003. 10.57262/ade/1366638680Suche in Google Scholar

[21] J. P. García Azorero and I. Peral Alonso, Existence and nonuniqueness for the p-Laplacian: Nonlinear eigenvalues, Comm. Partial Differential Equations 12 (1987), no. 12, 1389–1430. 10.1080/03605308708820534Suche in Google Scholar

[22] S. Kawai and N. Nakauchi, The first eigenvalue of the p-Laplacian on a compact Riemannian manifold, Nonlinear Anal. 55 (2003), no. 1–2, 33–46. 10.1016/S0362-546X(03)00209-8Suche in Google Scholar

[23] B. Kawohl and V. Fridman, Isoperimetric estimates for the first eigenvalue of the p-Laplace operator and the Cheeger constant, Comment. Math. Univ. Carolin. 44 (2003), no. 4, 659–667. Suche in Google Scholar

[24] E. H. Lieb and M. Loss, Analysis, Grad. Stud. Math. 14, American Mathematical Society, Providence, 2007. Suche in Google Scholar

[25] B. P. Lima, J. F. Montenegro and N. L. Santos, Eigenvalues estimates for the first eigenvalue of the p-Laplace operator on manifolds, preprint (2008), https://arxiv.org/abs/0808.2028. Suche in Google Scholar

[26] P. Lindqvist, On the equation div⁢(|∇⁡u|p-2⁢∇⁡u)+λ⁢|u|p-2⁢u=0, Proc. Amer. Math. Soc. 109 (1990), no. 1, 157–164. 10.2307/2048375Suche in Google Scholar

[27] J. Mao, Eigenvalue inequalities for the p-Laplacian on a Riemannian manifold and estimates for the heat kernel, J. Math. Pures Appl. (9) 101 (2014), no. 3, 372–393. 10.1016/j.matpur.2013.06.006Suche in Google Scholar

[28] A.-M. Matei, First eigenvalue for the p-Laplace operator, Nonlinear Anal. 39 (2000), no. 8, 1051–1068. 10.1016/S0362-546X(98)00266-1Suche in Google Scholar

[29] E. Parini, An introduction to the Cheeger problem, Surv. Math. Appl. 6 (2011), 9–21. Suche in Google Scholar

[30] A. Taheri, Function Spaces and Partial Differential Equations. I, Oxford Lecture Ser. Math. Appl. 40, Oxford University, Oxford, 2015. 10.1093/acprof:oso/9780198733133.001.0001Suche in Google Scholar

[31] A. Taheri, Function Spaces and Partial Differential Equations. II, Oxford Lecture Ser. Math. Appl. 41, Oxford University, Oxford, 2015. 10.1093/acprof:oso/9780198733133.001.0001Suche in Google Scholar

[32] H. Takeuchi, On the first eigenvalue of the p-Laplacian in a Riemannian manifold, Tokyo J. Math. 21 (1998), no. 1, 135–140. 10.3836/tjm/1270041991Suche in Google Scholar

[33] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984), no. 1, 126–150. 10.1016/0022-0396(84)90105-0Suche in Google Scholar