Positive solutions for a degenerate Kirchhoff problem. Issue 3 (19th August 2021) - Arcoya, David; Santos Júnior, João R.; Suárez, Antonio
Abstract: By assuming that the Kirchhoff term has $K$ degeneracy points and other appropriated conditions, we have proved the existence of at least $K$ positive solutions other than those obtained in Santos Júnior and Siciliano [Positive solutions for a Kirchhoff problem with vanishing nonlocal term, J. Differ. Equ. 265 (2018), 2034–2043], which also have ordered $H_{0}^{1}(Ω )$ -norms. A concentration phenomena of these solutions is verified as a parameter related to the area of a region under the graph of the reaction term goes to zero.