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Existence and concentration of solutions for a Kirchhoff type problem with potentials
Exact behavior of positive solutions to elliptic equations with multi-singular inverse square potentials
1. | School of Mathematical and Statistics, Jiangsu Normal University, Xuzhou 221116 |
2. | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China |
3. | School of Mathematical and Statistical Sciences, University of Texas-Rio Grande Valley, Edinburg, TX 78539 |
References:
[1] |
D. Cao and P. Han, Solutions to critical elliptic equations with multi-singular inverse square potentials, J. Differential Equations, 224 (2006), 332-372.
doi: 10.1016/j.jde.2005.07.010. |
[2] |
F. C. Cîrstea, A complete classification of the isolated singularities for nonlinear elliptic equations with inverse square potentials, Memoirs of AMS, 227 (2014), vi+85 pp. |
[3] |
F.C. Cîrstea and Y. Du, Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity, J. Funct. Anal., 250 (2007), 317-346.
doi: 10.1016/j.jfa.2007.05.005. |
[4] |
F.C. Cîrstea and Y. Du, Isolated singularities for weighted quasilinear elliptic equations, J. Funct. Anal., 259 (2010), 174-202.
doi: 10.1016/j.jfa.2010.03.015. |
[5] |
Y. Du, Order Structure and Topological Methods in Nonlinear Partial Differential Equations, Vol I: Maximum principle and applications, World Scientific Publishing, 2006.
doi: 10.1142/9789812774446. |
[6] |
Y. Du and Z. M. Guo, The degenerate logistic model and a singularly mixed boundary blow-up problem, Disrete Conin. Dyn. Syst., 14 (2006), 1-29. |
[7] |
Y. Du and L. Ma, Logistic type equations on $\mathbbR^N$ by a squeezing method involving boundary blow-up solutions, J. London Math. Soc., 64 (2001), 107-124.
doi: 10.1017/S0024610701002289. |
[8] |
M. Marcus and L. Véron, Existence and uniqueness results for large solutions of general nonlinear elliptic equations, J. Evol. Equ., 3 (2003), 637-652.
doi: 10.1007/s00028-003-0122-y. |
[9] |
L. Wei and Y. Du, Exact singular behavior of positive solutions to nonlinear elliptic equations with a Hardy potential, J. Lond. Math. Soc., 91 (2015), 731-749.
doi: 10.1112/jlms/jdv003. |
[10] |
L. Wei and Z. Feng, Isolated singularity for semilinear elliptic equations, Discrete Contin. Dyn. Syst., 35 (2015), 3239-3252.
doi: 10.3934/dcds.2015.35.3239. |
show all references
References:
[1] |
D. Cao and P. Han, Solutions to critical elliptic equations with multi-singular inverse square potentials, J. Differential Equations, 224 (2006), 332-372.
doi: 10.1016/j.jde.2005.07.010. |
[2] |
F. C. Cîrstea, A complete classification of the isolated singularities for nonlinear elliptic equations with inverse square potentials, Memoirs of AMS, 227 (2014), vi+85 pp. |
[3] |
F.C. Cîrstea and Y. Du, Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity, J. Funct. Anal., 250 (2007), 317-346.
doi: 10.1016/j.jfa.2007.05.005. |
[4] |
F.C. Cîrstea and Y. Du, Isolated singularities for weighted quasilinear elliptic equations, J. Funct. Anal., 259 (2010), 174-202.
doi: 10.1016/j.jfa.2010.03.015. |
[5] |
Y. Du, Order Structure and Topological Methods in Nonlinear Partial Differential Equations, Vol I: Maximum principle and applications, World Scientific Publishing, 2006.
doi: 10.1142/9789812774446. |
[6] |
Y. Du and Z. M. Guo, The degenerate logistic model and a singularly mixed boundary blow-up problem, Disrete Conin. Dyn. Syst., 14 (2006), 1-29. |
[7] |
Y. Du and L. Ma, Logistic type equations on $\mathbbR^N$ by a squeezing method involving boundary blow-up solutions, J. London Math. Soc., 64 (2001), 107-124.
doi: 10.1017/S0024610701002289. |
[8] |
M. Marcus and L. Véron, Existence and uniqueness results for large solutions of general nonlinear elliptic equations, J. Evol. Equ., 3 (2003), 637-652.
doi: 10.1007/s00028-003-0122-y. |
[9] |
L. Wei and Y. Du, Exact singular behavior of positive solutions to nonlinear elliptic equations with a Hardy potential, J. Lond. Math. Soc., 91 (2015), 731-749.
doi: 10.1112/jlms/jdv003. |
[10] |
L. Wei and Z. Feng, Isolated singularity for semilinear elliptic equations, Discrete Contin. Dyn. Syst., 35 (2015), 3239-3252.
doi: 10.3934/dcds.2015.35.3239. |
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