Geodesic
On a Positive Solution for (p,q)-Laplace Equation with Indefinite Weight
Minimax theory and its applications, Tome 1 (2016) no. 1
Cet article a éte moissonné depuis la source Minimax Theory and its Applications website

Voir la notice de l'article

This paper provides existence and non-existence results for a positive solution of the quasilinear elliptic equation −∆pu−μ∆qu=λ(mp(x)|u|p−2u+μmq(x)|u|q−2u) in Ω driven by the nonhomogeneous operator (p,q)-Laplacian under Dirichlet boundary condition, with μ > 0 and 1 < q < p < ∞. We show that in the case where μ > 0 the results are completely different from those for the usual eigenvalue problem for the p-Laplacian, which is retrieved when μ = 0. For instance, we prove that when μ > 0 there exists an interval of eigenvalues. Existence of positive solutions is obtained in resonant cases, too. A non-existence result is also given.
Mots-clés : (p,q)-Laplacian, nonlinear eigenvalue problems, indefinite weight, mountain pass theorem, global minimizer 
@article{MTA_2016_1_1_a0,
     author = {Dumitru Motreanu,Mieko Tanaka},
     title = {On a {Positive} {Solution} for {(p,q)-Laplace} {Equation} with {Indefinite} {Weight}},
     journal = {Minimax theory and its applications},
     year = {2016},
     volume = {1},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/MTA_2016_1_1_a0/}
}
TY  - JOUR
AU  - Dumitru Motreanu,Mieko Tanaka
TI  - On a Positive Solution for (p,q)-Laplace Equation with Indefinite Weight
JO  - Minimax theory and its applications
PY  - 2016
VL  - 1
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MTA_2016_1_1_a0/
ID  - MTA_2016_1_1_a0
ER  - 
%0 Journal Article
%A Dumitru Motreanu,Mieko Tanaka
%T On a Positive Solution for (p,q)-Laplace Equation with Indefinite Weight
%J Minimax theory and its applications
%D 2016
%V 1
%N 1
%U http://geodesic.mathdoc.fr/item/MTA_2016_1_1_a0/
%F MTA_2016_1_1_a0
Dumitru Motreanu,Mieko Tanaka. On a Positive Solution for (p,q)-Laplace Equation with Indefinite Weight. Minimax theory and its applications, Tome 1 (2016) no. 1. http://geodesic.mathdoc.fr/item/MTA_2016_1_1_a0/