The first eigenvalue and eigenfunction of a nonlinear elliptic system

0505711 - MÚ 2020 RIV NL eng J - Journal Article
Bozorgnia, F. - Seyyedi, M. - Vejchodský, Tomáš
The first eigenvalue and eigenfunction of a nonlinear elliptic system.
Applied Numerical Mathematics. Roč. 145, November (2019), s. 159-174. ISSN 0168-9274. E-ISSN 1873-5460
Institutional support: RVO:67985840
Keywords : nonlinear elliptic system * p-Laplacian * eigenvalue problem
OECD category: Pure mathematics
Impact factor: 1.979, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1016/j.apnum.2019.06.004

In this paper, we study the first eigenvalue of a nonlinear elliptic system involving p-Laplacian as the differential operator. The principal eigenvalue of the system and the corresponding eigenfunction are investigated both analytically and numerically. An alternative proof to show the simplicity of the first eigenvalue is given. In addition, the upper and lower bounds of the first eigenvalue are provided. Then, a numerical algorithm is developed to approximate the principal eigenvalue. This algorithm generates a decreasing sequence of positive numbers and various examples numerically indicate its convergence. Further, the algorithm is generalized to a class of gradient quasilinear elliptic systems.
Permanent Link: http://hdl.handle.net/11104/0297125