Existence and concentration results for the general Kirchhoff-type equations. (English) Zbl 1507.35017
The authors use the penalization method due to Del Pino and Felmer in order to prove the existence of single-peak or multi-peak solution for a nonlocal problem involving the Kirchhoff term. Such solutions concentrating around topologically stable critical points of a potential.
The results that can be found in this article give an affirmative answer to an open problem raised by G. M. Figueiredo et al. [Arch. Ration. Mech. Anal. 213, No. 3, 931–979 (2014; Zbl 1302.35356)].
The results that can be found in this article give an affirmative answer to an open problem raised by G. M. Figueiredo et al. [Arch. Ration. Mech. Anal. 213, No. 3, 931–979 (2014; Zbl 1302.35356)].
Reviewer: Giovany Malcher Figueiredo (Brasília)
MSC:
| 35B25 | Singular perturbations in context of PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35J62 | Quasilinear elliptic equations |
| 35R09 | Integro-partial differential equations |
Citations:
Zbl 1302.35356References:
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