Geodesic
Nonlinear curl-curl problems in \(\mathbb{R}^3\)
Minimax theory and its applications, Tome 7 (2022) no. 2
Cet article a éte moissonné depuis la source Minimax Theory and its Applications website

Voir la notice de l'article

We survey recent results concerning ground states and bound states u: R3 → R3 to the curl-curl problem ∇×(∇×u)+V(x)u=f(x,u) in R3, which originates from the nonlinear Maxwell equations. The energy functional associated with this problem is strongly indefinite due to the infinite dimensional kernel of ∇×(∇×·). The growth of the nonlinearity f is superlinear and subcritical at infinity or purely critical and we demonstrate a variational approach to the problem involving the generalized Nehari manifold. We also present some refinements of known results.
Mots-clés : Time-harmonic Maxwell equations, ground state, variational methods, strongly indefi nite functional, curl-curl problem, Orlicz spaces, N-functions 
@article{MTA_2022_7_2_a7,
     author = {Jaros{\l}aw Mederski and Jacopo Schino},
     title = {Nonlinear curl-curl problems in {\(\mathbb{R}^3\)}},
     journal = {Minimax theory and its applications},
     year = {2022},
     volume = {7},
     number = {2},
     zbl = {1490.35472},
     url = {http://geodesic.mathdoc.fr/item/MTA_2022_7_2_a7/}
}
TY  - JOUR
AU  - Jarosław Mederski
AU  - Jacopo Schino
TI  - Nonlinear curl-curl problems in \(\mathbb{R}^3\)
JO  - Minimax theory and its applications
PY  - 2022
VL  - 7
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MTA_2022_7_2_a7/
ID  - MTA_2022_7_2_a7
ER  - 
%0 Journal Article
%A Jarosław Mederski
%A Jacopo Schino
%T Nonlinear curl-curl problems in \(\mathbb{R}^3\)
%J Minimax theory and its applications
%D 2022
%V 7
%N 2
%U http://geodesic.mathdoc.fr/item/MTA_2022_7_2_a7/
%F MTA_2022_7_2_a7
Jarosław Mederski; Jacopo Schino. Nonlinear curl-curl problems in \(\mathbb{R}^3\). Minimax theory and its applications, Tome 7 (2022) no. 2. http://geodesic.mathdoc.fr/item/MTA_2022_7_2_a7/