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May  2013, 33(5): 2139-2154. doi: 10.3934/dcds.2013.33.2139

Resonance problems for Kirchhoff type equations

Jijiang Sun 1, and  Chun-Lei Tang 1,

1. 

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received  December 2011 Revised  June 2012 Published  December 2012

The existence of weak solutions is obtained for some Kirchhoff type equations with Dirichlet boundary conditions which are resonant at an arbitrary eigenvalue under a Landesman-Lazer type condition by the minimax methods.
Keywords: Resonance, critical point, Landesman-Lazer type condition, Kirchhoff type problem, link..
Mathematics Subject Classification: Primary: 35J60; Secondary: 47J10,35A1.
Citation: Jijiang Sun, Chun-Lei Tang. Resonance problems for Kirchhoff type equations. Discrete & Continuous Dynamical Systems, 2013, 33 (5) : 2139-2154. doi: 10.3934/dcds.2013.33.2139
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show all references

References:
[1]

Indiana Univ. Math. J., 25 (1976), 933-944.  Google Scholar

[2]

Comput. Math. Appl., 49 (2005), 85-93. doi: 10.1016/j.camwa.2005.01.008.  Google Scholar

[3]

Nonlinear Anal., 7 (1983), 981-1012. doi: 10.1016/0362-546X(83)90115-3.  Google Scholar

[4]

J. Math. Anal. Appl., 245 (2000), 7-19. doi: 10.1006/jmaa.2000.6713.  Google Scholar

[5]

J. Differential Equations, 250 (2011), 1876-1908. doi: 10.1016/j.jde.2010.11.017.  Google Scholar

[6]

J. Math Anal. Appl., 127 (1987), 435-442. doi: 10.1016/0022-247X(87)90121-1.  Google Scholar

[7]

J. Funct. Anal., 169 (1999), 189-200. doi: 10.1006/jfan.1999.3501.  Google Scholar

[8]

J. Math. Anal. Appl., 129 (1988), 482-492. doi: 10.1016/0022-247X(88)90266-1.  Google Scholar

[9]

J. Differential Equations, 252 (2011), 1813-1834. doi: 10.1016/j.jde.2011.08.035.  Google Scholar

[10]

J. Math. Mech., 19 (1970), 609-623.  Google Scholar

[11]

Appl. Math. Lett., 16 (2003), 243-248. doi: 10.1016/S0893-9659(03)80038-1.  Google Scholar

[12]

Nonlinear Anal., 70 (2009), 1275-1287. doi: 10.1016/j.na.2008.02.011.  Google Scholar

[13]

Proc. Amer. Math. Soc., 93 (1985), 667-674. doi: 10.2307/2045542.  Google Scholar

[14]

in: Applied Mathematical Sciences, 74, Springer-Verlag, New York, 1989.  Google Scholar

[15]

J. Math. Anal. Appl., 345 (2008), 511-521. doi: 10.1016/j.jmaa.2008.04.001.  Google Scholar

[16]

J. Differential Equations, 221 (2006), 246-255. doi: 10.1016/j.jde.2005.03.006.  Google Scholar

[17]

CBMS Regional Conference Series in Mathematics, 65, American Mathematical Society, Providence, RI, 1986.  Google Scholar

[18]

Nonlinear Anal., 16 (1991), 455-477. doi: 10.1016/0362-546X(91)90070-H.  Google Scholar

[19]

Nonlinear Anal., 64 (2006), 2007-2021. doi: 10.1016/j.na.2005.07.035.  Google Scholar

[20]

$3^{rd}$ Edition, Springer-Verlag, Berlin, 2000.  Google Scholar

[21]

Nonlinear Anal., 74 (2011), 1212-1222. doi: 10.1016/j.na.2010.09.061.  Google Scholar

[22]

J. Math. Anal. Appl., 216 (1997), 368-374. doi: 10.1006/jmaa.1997.5664.  Google Scholar

[23]

J. Math. Anal. Appl., 219 (1998), 110-124. doi: 10.1006/jmaa.1997.5793.  Google Scholar

[24]

Nonlinear Anal., 44 (2001), 323-335. doi: 10.1016/S0362-546X(99)00266-7.  Google Scholar

[25]

Nonlinear Anal., 10 (1986), 207-213. doi: 10.1016/0362-546X(86)90047-7.  Google Scholar

[26]

J. Math. Anal. Appl., 264 (2001), 133-146. doi: 10.1006/jmaa.2001.7660.  Google Scholar

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J. Math. Anal. Appl., 317 (2006), 456-463. doi: 10.1016/j.jmaa.2005.06.102.  Google Scholar

[28]

Nonlinear Anal., 72 (2010), 1019-1030. doi: 10.1016/j.na.2009.07.043.  Google Scholar

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