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Existence results and strong maximum principle for a resonant sublinear elliptic problem
Minimax theory and its applications, Tome 4 (2019) no. 2
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Let Ω be a bounded smooth connected open set in RN and let λ1 be the first eigenvalue of the Laplacian on Ω. We study the resonant elliptic problem    −∆u=λ1u+us−1−μur−1, u ≥0, u|∂Ω = 0 in Ω in Ω where s ∈]1,2[, r ∈]1,s[, and μ ∈]0,+∞[. An existence result of nonzero solutions is established via minimax and perturbation methods. Furthermore, for μ large enough, we prove a Strong Maximum Principle for the solutions of this problem. In particular, we extend to higher dimension an analogous recent result obtained in the one-dimensional case via the time-mapping method
Mots-clés : Sublinear elliptic problem, resonance, nonnegative solution, positive solution, mini max method, mountain pass, strong maximum principle 
@article{MTA_2019_4_2_a0,
     author = {Giovanni Anello},
     title = {Existence results and strong maximum principle for a resonant sublinear elliptic problem},
     journal = {Minimax theory and its applications},
     year = {2019},
     volume = {4},
     number = {2},
     zbl = {1432.35069},
     url = {http://geodesic.mathdoc.fr/item/MTA_2019_4_2_a0/}
}
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AU  - Giovanni Anello
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JO  - Minimax theory and its applications
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UR  - http://geodesic.mathdoc.fr/item/MTA_2019_4_2_a0/
ID  - MTA_2019_4_2_a0
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%J Minimax theory and its applications
%D 2019
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%U http://geodesic.mathdoc.fr/item/MTA_2019_4_2_a0/
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Giovanni Anello. Existence results and strong maximum principle for a resonant sublinear elliptic problem. Minimax theory and its applications, Tome 4 (2019) no. 2. http://geodesic.mathdoc.fr/item/MTA_2019_4_2_a0/