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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Jiu Liu 1; Jia-Feng Liao 2; Hui-Lan Pan 3; Chun-Lei Tang 4

@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 -
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] Remarks on non homogeneous elliptic Kirchhoff equations, NoDEA, Nonlinear Differ. Equ. Appl., Volume 23 (2016) no. 6, 57, 11 pages | DOI | MR | Zbl
[2] Positive solutions of elliptic Kirchhoff equations, Adv. Nonlinear Stud., Volume 17 (2017) no. 1, pp. 3-15 | DOI | MR | Zbl
[3] Dual variational methods in critical point theory and applications, J. Funct. Anal., Volume 14 (1973), pp. 349-381 | DOI | MR | Zbl
[4] 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] On the variational principle, J. Math. Anal. Appl., Volume 47 (1974), pp. 324-353 | DOI | MR | Zbl
[6] Some remarks on the comparison principle in Kirchhoff equations, Rev. Mat. Iberoam., Volume 34 (2018) no. 2, pp. 609-620 | DOI | MR | Zbl
[7] 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] 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] 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] 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] Progress in nonlinear Kirchhoff problems [Editorial], Nonlinear Anal., Theory Methods Appl., Volume 186 (2019), pp. 1-5 | DOI | MR | Zbl
[12] 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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