Multi-peak solutions to Kirchhoff equations in R3 with general nonlinearity

Local uniqueness of multi-peak solutions to a class of Kirchhoff equations

“…The first one was obtained by Luo et al [22], where the authors found the right limiting problem for the first time, and then they established some nondegeneracy result, which allows them to apply Lyapunov-Schmidt reduction method to obtain multi-peak solutions. Another result of multi-peak solutions for Kirchhoff equations with general nonlinearity can be found in the quite recent work [19] of Hu and Shuai.…”

Existence of multi-bump solutions for a nonlinear Kirchhoff equation

“…In [23], Luo, Peng, Wang, and Xiang proved the existence of positive multi-peak positive solutions of (1.4) when V (x) satisfies some suitable assumptions. In [13], Hu and Shuai also obtained multiple positive solutions to this type of perturbation problem with general nonlinearity under some precise hypotheses. Recently, Liu [20] investigated the existence of multi-bump solutions for the following Kirchhoff equation…”

Multi‐peak solutions of Kirchhoff equations involving subcritical or critical Sobolev exponents

“…Luo et al showed that possesses a ‐peak solution concentrating around by applying the Lyapunov‐Schmidt reduction method. Hu and Shuai extended this result to some general satisfying the Berestycki‐Lions–type conditions.…”

“…As reviewed above, the peak solutions obtained in the literature all concentrate around the minimal points of , and the peak solutions which concentrate at other type critical points of are not involved. Moreover, for the case where or is in critical growth, up to now, it is still unclear on the existence of multi‐peak solutions for Equations or .…”