Multiplicity of Solutions for an Elliptic Kirchhoff Equation Arcoya Álvarez, David Carmona Tapia, José Martínez Aparicio, Pedro J. Elliptic Kirchhoff equation Continua of solutions Multiplicity of solutions Research supported by Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI) and (FEDER) Fondo Europeo de Desarrollo Regional under Research Project PGC2018-096422-B-I00 and Junta de Andalucía, Consejería de Transformación Económica, Industria, Conocimiento y Universidades-Unión Europea grant P18-FR-667. First and third author supported by Junta de Andalucía FQM-116. Second author supported by Junta de Andalucía FQM-194 and CDTIME. Third author supported by Junta de Andalucía, Consejería de Transformación Económica, Industria, Conocimiento y Universidades grant UAL2020-FQM-B2046. In this paper we study the existence of positive solution to the Kirchhoff elliptic problem {−(1+γG′(∥∇u∥2L2(Ω)))Δu=λf(u)u=0 in Ω, on ∂Ω, where Ω is an open, bounded subset of RN (N≥3), f is a locally Lipschitz continuous real function, f(0)≥0, G′∈C(R+) and G′≥0. We prove the existence of at least two solutions with L∞(Ω) norm between two consecutive zeroes of f for large λ. 2022-09-29T06:47:27Z 2022-09-29T06:47:27Z 2022-09-28 journal article Arcoya, D., Carmona, J. & Martínez-Aparicio, P.J. Multiplicity of Solutions for an Elliptic Kirchhoff Equation. Milan J. Math. (2022). [https://doi.org/10.1007/s00032-022-00365-y] https://hdl.handle.net/10481/77066 10.1007/s00032-022-00365-y eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Springer Nature