The Fredholm alternative for the p-Laplacian in exterior domains

Authors: Pavel Drábek, Abhishek Sarkar, Hồ Ngọc Kỳ (Ky Ho),

https://doi.org/10.1016/j.na.2018.04.006

Publisher, magazine: ,

Publication year: 2018

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Abstract

We investigate the Fredholm alternative for the p-Laplacian in an exterior domain which is the complement of the closed unit ball in (). By employing techniques of Calculus of Variations we obtain the multiplicity of solutions. The striking difference between our case and the entire space case is also discussed.

Tags: p-Laplacian, Fredholm alternative, The first eigenvalue, Exterior domain, Variational method