Properties of minimizers for L 2 -subcritical Kirchhoff energy functionals
Helin Guo, Lingling Zhao · Advances in Nonlinear Analysis · 2025
Abstract We consider the properties of minimizers for the following constraint minimization problem: i ( c ) ≔ inf u ∈ S 1 I c ( u ) , i\left(c):= \mathop{\inf }\limits_{u\in {S}_{1}}{I}_{c}\left(u), where the L 2 {L}^{2} -unite sphere S 1 = { u ∈ H 1 ( R N ) ∣ ∫ R N V ( x ) u 2 d x < + ∞ , ‖ u ‖ L 2 = 1 } , {S}_{1}=\left\{u\in {H}^{1}\left({{\mathbb{R}}}^{N})| {\int }_{{{\mathbb{R}}}^{N}}V\left(x){u}^{2}{\rm{d}}x\lt +\infty ,{\Vert u\Vert }_{{L}^{2}}=1\right\}, and the energy functional I c ( u ) {I}_{c}\left(u) is defined by I