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Existence and nonexistence of positive solutions to an integral system involving Wolff potential
Boundary value problems for a semilinear elliptic equation with singular nonlinearity
1. | Department of Mathematics, Henan Normal University, Xinxiang, 453007, China |
References:
[1] |
P. Esposito, N. Ghoussoub and Y. Guo, Compactness along the branch of semi-stable and unstable solutions for an elliptic problem with a singular nonlinearity, Comm. Pure Appl. Math., LX (2007), 1731-1768.
doi: 10.1002/cpa.20189. |
[2] |
G. Flores, G. A. Mercado and J. A. Pelesko, Dynamics and touchdown in electrostatic MEMS, Proceedings of ICMEMS, (2003), 182-187. |
[3] |
N. Ghoussoub and Y. Guo, On the partial differential equations of electrostatic MEMS devices: stationary case, SIAM J. Math.Anal., 38 (2007), 1423-1449.
doi: 10.1137/050647803. |
[4] |
Z. M. Guo and L. Ma, Finite Morse index steady states of van der Waals force driven thin film equations, J. Math. Anal. Appl., 368 (2010), 559-572.
doi: 10.1016/j.jmaa.2010.04.012. |
[5] |
Z. M. Guo and X. Z. Peng, On the structure of positive solutions to an elliptic problem with a singular nonlinearity, J. Math. Anal.Appl., 354 (2009), 134-146.
doi: 10.1016/j.jmaa.2009.01.001. |
[6] |
Z. M. Guo and J. C. Wei, Ausdorff dimension of ruptures for solutions of a semilinear elliptic equation with singular nonlinearity, Manuscripta Math., 120 (2006), 193-209.
doi: 10.1007/s00229-006-0001-2. |
[7] |
Z. M. Guo and J. C. Wei, Symmetry of non-negative solutions of a semilinear elliptic equation with singular nonlinearity, Proc. R. Soc. Edinburgh, 137A (2007), 963-994.
doi: 10.1017/S0308210505001083. |
[8] |
Z. M. Guo and J. C. Wei, The Cauchy problem for a reaction-diffusion equation with a singular nonlinearity, J. Differential Equations, 240 (2007), 279-323.
doi: 10.1016/j.jde.2007.06.012. |
[9] |
Z. M. Guo and J. C. Wei, Infinitely many turning points for an elliptic problem with a singular nonlinearity, J. London Math. Soc., 78 (2008), 21-35.
doi: 10.1112/jlms/jdm121. |
[10] |
Z. M. Guo and D. Ye and F. Zhou, Existence of singular positive solutions for some semilinear elliptic equations, Pacific J. Math., 236 (2008), 57-71.
doi: 10.2140/pjm.2008.236.57. |
[11] |
H. Jiang and W. M. Ni, On steady states of van der Waals force driven thin film equations, European J. Appl. Math., 18 (2007), 153-180.
doi: 10.1017/S0956792507006936. |
[12] |
F. H. Lin and Y. S. Yang, Nonlinear non-local elliptic equation modelling electrostatic actuation, Proc. R. Soc. Lond., Ser. A Math. Phys. Eng. Sci., 463 (2007), 1323-1337.
doi: 10.1098/rspa.2007.1816. |
[13] |
L. Ma and J. C. Wei, Properties of positive solutions to an elliptic equation with negative exponent, J. Funct. Anal., 254 (2008), 1058-1087.
doi: 10.1016/j.jfa.2007.09.017. |
[14] |
J. A. Pelesko, Mathematical modeling of electrostatic MEMS with tailored dielectric properties, SIAM J. Appl. Math., 62 (2002), 888-908.
doi: 10.1137/S0036139900381079. |
[15] |
J. A. Pelesko and D. H. Bernstein, Modeling MEMS and NEMS, Chapman Hall and CRC press, 2002. |
show all references
References:
[1] |
P. Esposito, N. Ghoussoub and Y. Guo, Compactness along the branch of semi-stable and unstable solutions for an elliptic problem with a singular nonlinearity, Comm. Pure Appl. Math., LX (2007), 1731-1768.
doi: 10.1002/cpa.20189. |
[2] |
G. Flores, G. A. Mercado and J. A. Pelesko, Dynamics and touchdown in electrostatic MEMS, Proceedings of ICMEMS, (2003), 182-187. |
[3] |
N. Ghoussoub and Y. Guo, On the partial differential equations of electrostatic MEMS devices: stationary case, SIAM J. Math.Anal., 38 (2007), 1423-1449.
doi: 10.1137/050647803. |
[4] |
Z. M. Guo and L. Ma, Finite Morse index steady states of van der Waals force driven thin film equations, J. Math. Anal. Appl., 368 (2010), 559-572.
doi: 10.1016/j.jmaa.2010.04.012. |
[5] |
Z. M. Guo and X. Z. Peng, On the structure of positive solutions to an elliptic problem with a singular nonlinearity, J. Math. Anal.Appl., 354 (2009), 134-146.
doi: 10.1016/j.jmaa.2009.01.001. |
[6] |
Z. M. Guo and J. C. Wei, Ausdorff dimension of ruptures for solutions of a semilinear elliptic equation with singular nonlinearity, Manuscripta Math., 120 (2006), 193-209.
doi: 10.1007/s00229-006-0001-2. |
[7] |
Z. M. Guo and J. C. Wei, Symmetry of non-negative solutions of a semilinear elliptic equation with singular nonlinearity, Proc. R. Soc. Edinburgh, 137A (2007), 963-994.
doi: 10.1017/S0308210505001083. |
[8] |
Z. M. Guo and J. C. Wei, The Cauchy problem for a reaction-diffusion equation with a singular nonlinearity, J. Differential Equations, 240 (2007), 279-323.
doi: 10.1016/j.jde.2007.06.012. |
[9] |
Z. M. Guo and J. C. Wei, Infinitely many turning points for an elliptic problem with a singular nonlinearity, J. London Math. Soc., 78 (2008), 21-35.
doi: 10.1112/jlms/jdm121. |
[10] |
Z. M. Guo and D. Ye and F. Zhou, Existence of singular positive solutions for some semilinear elliptic equations, Pacific J. Math., 236 (2008), 57-71.
doi: 10.2140/pjm.2008.236.57. |
[11] |
H. Jiang and W. M. Ni, On steady states of van der Waals force driven thin film equations, European J. Appl. Math., 18 (2007), 153-180.
doi: 10.1017/S0956792507006936. |
[12] |
F. H. Lin and Y. S. Yang, Nonlinear non-local elliptic equation modelling electrostatic actuation, Proc. R. Soc. Lond., Ser. A Math. Phys. Eng. Sci., 463 (2007), 1323-1337.
doi: 10.1098/rspa.2007.1816. |
[13] |
L. Ma and J. C. Wei, Properties of positive solutions to an elliptic equation with negative exponent, J. Funct. Anal., 254 (2008), 1058-1087.
doi: 10.1016/j.jfa.2007.09.017. |
[14] |
J. A. Pelesko, Mathematical modeling of electrostatic MEMS with tailored dielectric properties, SIAM J. Appl. Math., 62 (2002), 888-908.
doi: 10.1137/S0036139900381079. |
[15] |
J. A. Pelesko and D. H. Bernstein, Modeling MEMS and NEMS, Chapman Hall and CRC press, 2002. |
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