Comptes Rendus
Équations aux dérivées partielles
A bifurcation-type result for Kirchhoff equations
Jiu Liu1 ; Jia-Feng Liao2 ; Hui-Lan Pan3 ; Chun-Lei Tang4 
1 School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun, Guizhou 558000, People’s Republic of China
2 School of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637002, People’s Republic of China
3 School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, People’s Republic of China
4 School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 247-254.

This paper deals with a class of Kirchhoff type elliptic Dirichlet boundary value problems where the combined effects of Kirchhoff term and nonlinear term allow us to establish a bifurcation-type result as the positive parameter varies.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.294
Classification : 35J60, 35J20
Jiu Liu 1 ; Jia-Feng Liao 2 ; Hui-Lan Pan 3 ; Chun-Lei Tang 4

1 School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun, Guizhou 558000, People’s Republic of China
2 School of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637002, People’s Republic of China
3 School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, People’s Republic of China
4 School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRMATH_2022__360_G3_247_0,
     author = {Jiu Liu and Jia-Feng Liao and Hui-Lan Pan and Chun-Lei Tang},
     title = {A bifurcation-type result for {Kirchhoff} equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {247--254},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.294},
     language = {en},
}
TY  - JOUR
AU  - Jiu Liu
AU  - Jia-Feng Liao
AU  - Hui-Lan Pan
AU  - Chun-Lei Tang
TI  - A bifurcation-type result for Kirchhoff equations
JO  - Comptes Rendus. Mathématique
PY  - 2022
SP  - 247
EP  - 254
VL  - 360
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.294
LA  - en
ID  - CRMATH_2022__360_G3_247_0
ER  - 
%0 Journal Article
%A Jiu Liu
%A Jia-Feng Liao
%A Hui-Lan Pan
%A Chun-Lei Tang
%T A bifurcation-type result for Kirchhoff equations
%J Comptes Rendus. Mathématique
%D 2022
%P 247-254
%V 360
%I Académie des sciences, Paris
%R 10.5802/crmath.294
%G en
%F CRMATH_2022__360_G3_247_0
Jiu Liu; Jia-Feng Liao; Hui-Lan Pan; Chun-Lei Tang. A bifurcation-type result for Kirchhoff equations. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 247-254. doi : 10.5802/crmath.294. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.294/

[1] Antonio Ambrosetti; David Arcoya Remarks on non homogeneous elliptic Kirchhoff equations, NoDEA, Nonlinear Differ. Equ. Appl., Volume 23 (2016) no. 6, 57, 11 pages | DOI | MR | Zbl

[2] Antonio Ambrosetti; David Arcoya Positive solutions of elliptic Kirchhoff equations, Adv. Nonlinear Stud., Volume 17 (2017) no. 1, pp. 3-15 | DOI | MR | Zbl

[3] Antonio Ambrosetti; Paul H. Rabinowitz Dual variational methods in critical point theory and applications, J. Funct. Anal., Volume 14 (1973), pp. 349-381 | DOI | MR | Zbl

[4] Henri Berestycki; Italo Capuzzo-Dolcetta; Louis Nirenberg Variational methods for indefinite superlinear homogeneous elliptic problems, NoDEA, Nonlinear Differ. Equ. Appl., Volume 2 (1995) no. 4, pp. 553-572 | DOI | MR | Zbl

[5] Ivar Ekeland On the variational principle, J. Math. Anal. Appl., Volume 47 (1974), pp. 324-353 | DOI | MR | Zbl

[6] Giovany M. Figueiredo; Antonio Suárez Some remarks on the comparison principle in Kirchhoff equations, Rev. Mat. Iberoam., Volume 34 (2018) no. 2, pp. 609-620 | DOI | MR | Zbl

[7] Zhanping Liang; Fuyi Li; Junping Shi Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 31 (2014) no. 1, pp. 155-167 | DOI | Numdam | MR | Zbl

[8] Zhanping Liang; Fuyi Li; Junping Shi Positive solutions of Kirchhoff-type non-local elliptic equation: a bifurcation approach, Proc. R. Soc. Edinb., Sect. A, Math., Volume 147 (2017) no. 4, pp. 875-894 | DOI | MR | Zbl

[9] Daisuke Naimen On the Brezis-Nirenberg problem with a Kirchhoff type perturbation, Adv. Nonlinear Stud., Volume 15 (2015) no. 1, pp. 135-156 | DOI | MR | Zbl

[10] Kanishka Perera; Zhitao Zhang Nontrivial solutions of Kirchhoff-type problems via the Yang index, J. Differ. Equations, Volume 221 (2006) no. 1, pp. 246-255 | DOI | MR | Zbl

[11] Patrizia Pucci; Vicenţiu D. Rădulescu Progress in nonlinear Kirchhoff problems [Editorial], Nonlinear Anal., Theory Methods Appl., Volume 186 (2019), pp. 1-5 | DOI | MR | Zbl

[12] Ji-Jiang Sun; Chun-Lei Tang Existence and multiplicity of solutions for Kirchhoff type equations, Nonlinear Anal., Theory Methods Appl., Volume 74 (2011) no. 4, pp. 1212-1222 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique