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Multiple positive solutions for Kirchhoff type problems with singularity
| 1. | Department of Mathematics, University of Chinese Academy of Sciences, Beijing 100049, P.R. China |
| 2. | Department of Mathematics, Graduate University of Chinese Academy of Sciences, Beijing 100049, China |
References:
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G. Anello, A uniqueness result for a nonlocal equation of Kirchhoff type and some related open problems, J. Math. Anal. Appl., 373 (2011), 248-251.
doi: 10.1016/j.jmaa.2010.07.019. |
| [2] |
C. Chen, Y. Kuo and T. Wu, The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions, J. Differential Equations, 250 (2011), 1876-1908.
doi: 10.1016/j.jde.2010.11.017. |
| [3] |
J. Graham-Eagle, A variational approach to upper and lower solutions, IMA J. Appl. Math., 44 (1990), 181-184.
doi: 10.1093/imamat/44.2.181. |
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X. He and W. Zou, Infinitely many solutions for Kirchhoff-type problems, Nonlinear Anal., 70 (2009), 1407-1414.
doi: 10.1016/j.na.2008.02.021. |
| [5] |
D. S. Kang, On the quasilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy terms, Nonlinear Anal., 68 (2008), 1973-1985.
doi: 10.1016/j.na.2007.01.024. |
| [6] |
B. Ricceri, On an elliptic Kirchhoff-type problem depending on two parameters, J. Global Optim., 46 (2010), 543-549.
doi: 10.1007/s10898-009-9438-7. |
| [7] |
Y. J. Sun and S. J. Li, Some remarks on a superlinear-singular problem: Estimates for $\lambda^*$, Nonlinear Anal., 69 (2008), 2636-2650.
doi: 10.1016/j.na.2007.08.037. |
| [8] |
Y. J. Sun, S. P. Wu and Y. M. Long, Combined effects of singular and superlinear nonlinearities in some singular boundary value problems, J. Differential Equations, 176 (2001), 511-531.
doi: 10.1006/jdeq.2000.3973. |
| [9] |
Y. J. Sun and S. P. Wu, An exact estimate result for a class of singular equations with critical exponents, J. Funct. Anal., 260 (2011), 1257-1284.
doi: 10.1016/j.jfa.2010.11.018. |
| [10] |
G. Talenti, Best constant in Sobolev inequality, Ann. Math. Pure Appl., 110 (1976), 353-372.
doi: 10.1007/BF02418013. |
| [11] |
Z. Zhang and K. Perera, Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow, J. Math. Anal. Appl., 317 (2006), 456-463.
doi: 10.1016/j.jmaa.2005.06.102. |
show all references
References:
| [1] |
G. Anello, A uniqueness result for a nonlocal equation of Kirchhoff type and some related open problems, J. Math. Anal. Appl., 373 (2011), 248-251.
doi: 10.1016/j.jmaa.2010.07.019. |
| [2] |
C. Chen, Y. Kuo and T. Wu, The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions, J. Differential Equations, 250 (2011), 1876-1908.
doi: 10.1016/j.jde.2010.11.017. |
| [3] |
J. Graham-Eagle, A variational approach to upper and lower solutions, IMA J. Appl. Math., 44 (1990), 181-184.
doi: 10.1093/imamat/44.2.181. |
| [4] |
X. He and W. Zou, Infinitely many solutions for Kirchhoff-type problems, Nonlinear Anal., 70 (2009), 1407-1414.
doi: 10.1016/j.na.2008.02.021. |
| [5] |
D. S. Kang, On the quasilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy terms, Nonlinear Anal., 68 (2008), 1973-1985.
doi: 10.1016/j.na.2007.01.024. |
| [6] |
B. Ricceri, On an elliptic Kirchhoff-type problem depending on two parameters, J. Global Optim., 46 (2010), 543-549.
doi: 10.1007/s10898-009-9438-7. |
| [7] |
Y. J. Sun and S. J. Li, Some remarks on a superlinear-singular problem: Estimates for $\lambda^*$, Nonlinear Anal., 69 (2008), 2636-2650.
doi: 10.1016/j.na.2007.08.037. |
| [8] |
Y. J. Sun, S. P. Wu and Y. M. Long, Combined effects of singular and superlinear nonlinearities in some singular boundary value problems, J. Differential Equations, 176 (2001), 511-531.
doi: 10.1006/jdeq.2000.3973. |
| [9] |
Y. J. Sun and S. P. Wu, An exact estimate result for a class of singular equations with critical exponents, J. Funct. Anal., 260 (2011), 1257-1284.
doi: 10.1016/j.jfa.2010.11.018. |
| [10] |
G. Talenti, Best constant in Sobolev inequality, Ann. Math. Pure Appl., 110 (1976), 353-372.
doi: 10.1007/BF02418013. |
| [11] |
Z. Zhang and K. Perera, Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow, J. Math. Anal. Appl., 317 (2006), 456-463.
doi: 10.1016/j.jmaa.2005.06.102. |
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