Nonlinear elliptic eigenvalue problems in cylindrical domains becoming unbounded in one direction

Article type: Research Article

Authors: Rawat, Rama | Roy, Haripada | Roy, Prosenjit^{; *}

Affiliations: Indian Institute of Technology, Kanpur, India

Correspondence: [*] Corresponding author. E-mail: prosenjit@iitk.ac.in.

Abstract: The aim of this work is to characterize the asymptotic behaviour of the first eigenfunction of the generalised p-Laplace operator with mixed (Dirichlet and Neumann) boundary conditions in cylindrical domains when the length of the cylindrical domains tends to infinity. This generalises an earlier work of Chipot et al. (Asymptot. Anal. 85(3–4) (2013) 199–227) where the linear case p=2 is studied. Asymptotic behavior of all the higher eigenvalues of the linear case and the second eigenvalues of general case (using topological degree) for such problems is also studied.

Keywords: p-Laplacian, uniform elliptcity, Poincaré inequality, Krasnoselskii’s genus

DOI: 10.3233/ASY-241907

Journal: Asymptotic Analysis, vol. 139, no. 3-4, pp. 245-277, 2024