|
[1]
|
Kirchhoff, G. (1883) Mechanik. Teubner, Leipzig.
|
|
[2]
|
Oplinger, D.W. (1960) Frequency Response of a Nonlinear Stretched String. The Journal of the Acoustical Society of America, 32, 1529-1538.
https://doi.org/10.1121/1.1907948
|
|
[3]
|
Lions, J.L. (1978) On Some Questions in Boundary Value Problems of Mathematical Physics. In: North-Holland Mathematics Studies, Vol. 30, North-Holland, Amsterdam, New York, 284- 346.
https://doi.org/10.1016/S0304-0208(08)70870-3
|
|
[4]
|
Alves, C.O. and Figueiredo, G.M. (2016) Multi-Bump Solutions for a Kirchhoff-Type Problem. dvances in Nonlinear Analysis, 5, 1-26.
https://doi.org/10.1515/anona-2015-0101
|
|
[5]
|
Deng, Y.B., Peng, S.J. and Shuai, W. (2015) Existence and Asymptotic Behavior of Nodal Solutions for the Kirchhoff-Type Problems in R3. Journal of Functional Analysis, 269, 3500- 3527.
https://doi.org/10.1016/j.jfa.2015.09.012
|
|
[6]
|
Deng, Y.B. and Shuai, W. (2018) Sign-Changing Multi-Bump Solutions for Kirchhoff-Type Equations in R3. Discrete and Continuous Dynamical Systems, 38, 3139-3168.
https://doi.org/10.3934/dcds.2018137
|
|
[7]
|
Figueiredo, G.M., Ikoma, N. and Santos Jr., J.R. (2014) Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities. Archive for Rational Mechanics and Analysis, 213, 931-979.
https://doi.org/10.1007/s00205-014-0747-8
|
|
[8]
|
Guo, Z. (2015) Ground State for Kirchhoff Equations without Compact Condition. Journal of Differential Equations, 259, 2884-2902.
https://doi.org/10.1016/j.jde.2015.04.005
|
|
[9]
|
He, X.M. and Zou, W.M. (2012) Existence and Concentration Behavior of Positive Solutions for a Kirchhoff Equation in R3. Journal of Differential Equations, 252, 1813-1834.
https://doi.org/10.1016/j.jde.2011.08.035
|
|
[10]
|
He, Y., Li, G.B. and Peng, S.J. (2014) Concentrating Bound States for Kirchhoff Type Prob- lems in R3 Involving Critical Sobolev Exponents. Advanced Nonlinear Studies, 14, 483-510.
https://doi.org/10.1515/ans-2014-0214
|
|
[11]
|
He, Y. and Li, G.B. (2015) Standing Waves for a Class of Kirchhoff Type Problems in R3 In- volving Critical Sobolev Exponents. Calculus of Variations and Partial Differential Equations, 54, 3067-3106.
https://doi.org/10.1007/s00526-015-0894-2
|
|
[12]
|
He, Y. (2016) Concentrating Bounded States for a Class of Singularly Perturbed Kirchhoff Type Equations with a General Nonlinearity. Journal of Differential Equations, 261, 6178- 6220.
https://doi.org/10.1016/j.jde.2016.08.034
|
|
[13]
|
Li, G.B. and Ye, H.Y. (2014) Existence of Positive Ground State Solutions for the Nonlinear Kirchhoff Type Equations in R3. Journal of Differential Equations, 257, 566-600.
https://doi.org/10.1016/j.jde.2014.04.011
|
|
[14]
|
Li, Y.H., Li, F.Y. and Shi, J.P. (2012) Existence of a Positive Solution to Kirchhoff Type Problems without Compactness Conditions. Journal of Differential Equations, 253, 2285-2294.
https://doi.org/10.1016/j.jde.2012.05.017
|
|
[15]
|
Mao, A. and Chang, H. (2016) Kirchhoff Type Problems in RN with Radial Potentials and Locally Lipschitz Functional. Applied Mathematics Letters, 62, 49-54.
https://doi.org/10.1016/j.aml.2016.06.014
|
|
[16]
|
Naimen, D. (2014) The Critical Problem of Kirchhoff Type Elliptic Equations in Dimension Four. Journal of Differential Equations, 257, 1168-1193.
https://doi.org/10.1016/j.jde.2014.05.002
|
|
[17]
|
Sun, J.T. and Wu, T.F. (2014) Ground State Solutions for an Indefinite Kirchhoff Type Prob- lem with Steep Potential Well. Journal of Differential Equations, 256, 1771-1792.
https://doi.org/10.1016/j.jde.2013.12.006
|
|
[18]
|
Tang, X.H. and Cheng, B. (2016) Ground State Sign-Changing Solutions for Kirchhoff Type Problems in Bounded Domains. Journal of Differential Equations, 261, 2384-2402.
https://doi.org/10.1016/j.jde.2016.04.032
|
|
[19]
|
Wang, D.B. (2020) Least Energy Sign-Changing Solutions of Kirchhoff-Type Equation with Critical Growth. Journal of Mathematical Physics, 61, Article ID: 011501.
https://doi.org/10.1063/1.5074163
|
|
[20]
|
Wang, J., Tian, L.X., Xu, J.X. and Zhang, F.B. (2012) Multiplicity and Concentration of Positive Solutions for a Kirchhoff Type Problem with Critical Growth. Journal of Differential Equations, 253, 2314-2351.
https://doi.org/10.1016/j.jde.2012.05.023
|
|
[21]
|
Xie, Q.L., Ma, S.W. and Zhang, X. (2016) Bound State Solutions of Kirchhoff Type Problems with Critical Exponent. Journal of Differential Equations, 261, 890-924.
https://doi.org/10.1016/j.jde.2016.03.028
|
|
[22]
|
Yu, X. (2010) Existence Results for a Schro¨dinger-Poisson Equation. Mathematica Applicata, 23, 648-652.
|
|
[23]
|
Willem, M. (1996) Minimax Theorems. Birkha¨user, Boston.
|