Positive solutions for a degenerate Kirchhoff problem. Issue 3 (19th August 2021)

• Record Type: Journal Article
• Authors: Arcoya, David; Santos Júnior, João R.; Suárez, Antonio
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 64:Issue 3(2021)
• Page Start: 675
• Page End: 688
• Publication Date: 2021-08-19
• Subjects: degenerate Kirchhoff problem -- variational methods -- concentration phenomena; 35J20 -- 35J25 -- 35Q74; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091521000444
• Languages: English
• ISSNs: 0013-0915

Abstract

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 $H_{0}^{1}(\Omega )$ -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.