This study focuses on the existence and concentration of ground state solutions for a class of fractional Kirchhoff–Schrödinger equations. We first study the problem

where \(s \in (0,1), N > 2s, [\cdot]_s\) is the Gagliardo semi-norm, \(\bar{c}\) is a suitable constant,M is a non-degenerate continuous Kirchhoff function that behaves like \(t^{\alpha}, V(x) = {\lambda}a(x) + 1, {\rm with}\,\, a(x) \geq 0\) and a is identically zero on the bounded set \({\Omega}_{\Upsilon}\) , and f denotes a continuous nonlinearity with subcritical growth at infinity. The proof relies on penalization arguments and variational methods to obtain the existence of a solution with minimal energy for a large value of \(\lambda\). Moreover, assuming that \(M(t) = m_{0} + b_{0}t^{\alpha}\) and utilizing the same techniques combined with a concentration-compactness lemma, we can establish the existence and concentration of solutions for the problem

if the value of \(\lambda\) is large enough and b₀ is small or m₀ is large.

这项研究集中于一类分数阶Kirchhoff-Schrödinger方程的基态解的存在和集中。我们首先研究问题

其中\（s \ in（0,1），N> 2s，[\ cdot] _s \）是Gagliardo半范数，\（\ bar {c} \）是合适的常数，M是非简并的连续的Kirchhoff函数，其行为类似于\（t ^ {\ alpha}，V（x）= {\ lambda} a（x）+ 1，{\ rm with} \，\，a（x）\ geq 0 \）和a在有界集\（{\ Omega} _ {\ Upsilon} \）上等于零，并且f表示连续的非线性，其中亚临界增长为无穷大。该证明依赖于惩罚参数和变分方法来获得存在较大能量\（\ lambda \）的最小能量解的存在。此外，假设\（M（t）= m_ {0} + b_ {0} t ^ {\ alpha} \） 并利用相同的技术结合浓度-紧致性引理，我们可以确定问题的解的存在性和集中性

如果\（\ lambda \）的值足够大且b ₀小或m ₀大。