Abstract
Let Ω ⊂ RN (N ≥ 2) be a simply connected bounded domain, containing the origin, with C2 boundary denoted by ∂Ω. Denote by
where p, q ∈ (1,N),
-
(Communicated by Alberto Lastra)
References
[1] ADAMS, R: Sobolev Spaces, Academic Press, New York, 1975.Search in Google Scholar
[2] BOCEA, M. — MIHĂILESCU, M.: Existence of nonnegative viscosity solutions for a class of problems involving the ∞-Laplacian, NoDEA Nonlinear Differential Equations Appl. 23 (2016), Art. ID 11.10.1007/s00030-016-0373-2Search in Google Scholar
[3] CHHETRI, M. — DRÁBEK, P.: Principal eigenvalue of p−Laplacian operator in exterior domain, Results Math. 66 (2014), 461–468.10.1007/s00025-014-0386-2Search in Google Scholar
[4] FĂRCĂŞEANU, M. — MIHĂILESCU, M. — STANCU-DUMITRU, D.: On the set of eigenvalues of some PDEs with homogeneous Neumann boundary condition, Nonlinear Anal. 116 (2015), 19–25.10.1016/j.na.2014.12.019Search in Google Scholar
[5] FUKAGAI, N. — ITO, M. — NARUKAWA, K.: Positive solutions of quasilinear elliptic equations with critical Orlicz-Sobolev nonlinearity on RN, Funkcial. Ekvac. 49 (2006), 235–267.10.1619/fesi.49.235Search in Google Scholar
[6] HARJULEHTO, P. — HÄSTÖ, P.: Orlicz Spaces and Generalized Orlicz Spaces. Lecture Notes in Math. 2236, Springer, Cham, 2019.10.1007/978-3-030-15100-3Search in Google Scholar
[7] LÊ, A.: Eigenvalue problems for the p-Laplacian, Nonlinear Anal. 64 (2006), 1057–1099.10.1016/j.na.2005.05.056Search in Google Scholar
[8] LINDQVIST, P.: A nonlinear eigenvalue problem. In: Topics in Mathematical Analysis (P. Ciatti et al., eds.), Ser. Anal. Appl. Comput. 3, Hackensack, NJ: World Scientific, 2008, pp. 175–203.10.1142/9789812811066_0005Search in Google Scholar
[9] MIHĂILESCU, M.: An eigenvalue problem possessing a continuous family of eigenvalues plus an isolated eigenvalue, Commun. Pure Appl. Anal. 10 (2011), 701–708.10.3934/cpaa.2011.10.701Search in Google Scholar
[10] MIHĂILESCU, M. — MOROŞANU, G.: Eigenvalues of −Δp−Δq under Neumann boundary condition, Canad. Math. Bull. 59 (2016), 606–616.10.4153/CMB-2016-025-2Search in Google Scholar
[11] MIHĂILESCU, M. — STANCU-DUMITRU, D.: A perturbed eigenvalue problem on general domains, Ann. Funct. Anal. 7 (2016), 529–542.10.1215/20088752-3660738Search in Google Scholar
[12] TANAKA, M.: Generalized eigenvalue problems forp, q)-Laplacian with indefinite weight, J. Math. Anal. Appl. 419 (2014), 1181–1192.10.1016/j.jmaa.2014.05.044Search in Google Scholar
© 2022 Mathematical Institute Slovak Academy of Sciences
