Goel, Divya; Sreenadh, K. On the second eigenvalue of combination between local and nonlocal \(p\)-Laplacian. (English) Zbl 1425.35131 Proc. Am. Math. Soc. 147, No. 10, 4315-4327 (2019). The mountain pass characterization of the second eigenvalue of the perturbed \(p\)-Laplacian operator is studied. The variational characterization of the second eigenvalue and the sharp lower bounds on the first and second eigenvalues is an open question. The authors prove the variational characterization of the second eigenvalue of the operator associated to the considered problem. In particular, they prove the Faber-Krahn inequality and the nonlocal Hong-Krahn-Szegő inequality. Reviewer: Stepan Agop Tersian (Rousse) Cited in 7 Documents MSC: 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 49Q10 Optimization of shapes other than minimal surfaces 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems 35P15 Estimates of eigenvalues in context of PDEs 35R11 Fractional partial differential equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:nonlocal p-Laplacian; eigenvalue problem; Faber-Krahn inequality; nonlocal Hong-Krahn-Szegő inequality PDFBibTeX XMLCite \textit{D. Goel} and \textit{K. Sreenadh}, Proc. Am. Math. Soc. 147, No. 10, 4315--4327 (2019; Zbl 1425.35131) Full Text: DOI arXiv References: [1] Ambrosetti, Antonio; Rabinowitz, Paul H., Dual variational methods in critical point theory and applications, J. Functional Analysis, 14, 349-381 (1973) · Zbl 0273.49063 [2] Almgren, Frederick J., Jr.; Lieb, Elliott H., Symmetric decreasing rearrangement is sometimes continuous, J. Amer. Math. 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