Geodesic
Elliptic problems with non Lipschitz nonlinearities: some recent results and open questions
Minimax theory and its applications, Tome 2 (2017) no. 1
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Let p ∈]1,+∞[, let r,s ∈]0,p[, with r < s, and let λ ∈]0,+∞[. In this paper, we present some recent existence and multiplicity results on the solutions of the Dirichlet problem for the elliptic equation −∆pu = (λ|u|s−2u−|u|r−2u)χ{u=0} in a bounded domain Ω ⊂ RN, with 0-boundary data. Some related open questions are also proposed.
Mots-clés : Elliptic boundary value problem, nonnegative solution, positive solution, least en ergy solution, least energy nodal solution, variational methods, indefinite nonlinearities 
@article{MTA_2017_2_1_a0,
     author = {Giovanni Anello},
     title = {Elliptic problems with non {Lipschitz} nonlinearities: some recent results and open questions},
     journal = {Minimax theory and its applications},
     year = {2017},
     volume = {2},
     number = {1},
     zbl = {1366.35025},
     url = {http://geodesic.mathdoc.fr/item/MTA_2017_2_1_a0/}
}
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Giovanni Anello. Elliptic problems with non Lipschitz nonlinearities: some recent results and open questions. Minimax theory and its applications, Tome 2 (2017) no. 1. http://geodesic.mathdoc.fr/item/MTA_2017_2_1_a0/