Ground-state solutions to a Kirchhoff-type transmission problem

Fuyi Li, Ying Zhang, Xiaoli Zhu, Zhanping Liang



In this paper, we consider the existence of ground-state solutions to nonlinear Kirchhoff-type transmission problems by using the methods from (Silvia Cingolani and Tobias Weth, {\it On the planar Schrödinger-Poisson system}, Ann. Inst. H. Poincaré Anal. Non Linéaire {\bf 33} (2016), no.\ 1, 169-197). Here, we avoid the conditions under which the nonlinear terms of $f$ and $g$ are forms of $C^1$. In particular, when $N=2$, the existence of ground-state solutions is established to the Kirchhoff-type transmission problem with exponent-type nonlinearity.


Kirchhoff-type; transmission problems; ground-state solutions

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