Partial differential equations
A bifurcation-type result for Kirchhoff equations
Comptes Rendus. Mathématique, Volume 360 (2022) no. G3, 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.

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DOI: 10.5802/crmath.294
Classification: 35J60, 35J20
Liu, Jiu 1; Liao, Jia-Feng 2; Pan, Hui-Lan 3; Tang, Chun-Lei 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
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Liu, Jiu; Liao, Jia-Feng; Pan, Hui-Lan; Tang, Chun-Lei. A bifurcation-type result for Kirchhoff equations. Comptes Rendus. Mathématique, Volume 360 (2022) no. G3, pp. 247-254. doi : 10.5802/crmath.294. http://www.numdam.org/articles/10.5802/crmath.294/

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

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

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

[4] Berestycki, Henri; Capuzzo-Dolcetta, Italo; Nirenberg, Louis 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] Ekeland, Ivar On the variational principle, J. Math. Anal. Appl., Volume 47 (1974), pp. 324-353 | DOI | MR | Zbl

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

[7] Liang, Zhanping; Li, Fuyi; Shi, Junping 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] Liang, Zhanping; Li, Fuyi; Shi, Junping 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] Naimen, Daisuke 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] Perera, Kanishka; Zhang, Zhitao 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] Pucci, Patrizia; Rădulescu, Vicenţiu D. Progress in nonlinear Kirchhoff problems [Editorial], Nonlinear Anal., Theory Methods Appl., Volume 186 (2019), pp. 1-5 | DOI | MR | Zbl

[12] Sun, Ji-Jiang; Tang, Chun-Lei 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

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