Multiplicity and asymptotic behavior of normalized solutions for fourth‐order equations of the Kirchhoff type

Abstract In this paper, we study the following fourth‐order equation of the Kirchhoff type under the normalized constraint , where are constants. and , where if and if . arises as a Lagrange multiplier. We obtain the existence of infinitely many radial solutions for or . Furthermore, we analyze the asymptotic behavior of normalized solutions obtained above with respect to the parameter . Our results extend and generalize some results of Bonheure et al. (Trans. Amer. Math. Soc. 372 (2019), no. 3) and Bonheure et al. (SIAM J. Math. Anal. 50 (2018)).