Remarks on an elliptic equation of Kirchhoff type

2005 ◽  
Vol 63 (5-7) ◽  
pp. e1967-e1977 ◽  
Author(s):  
T.F. Ma
Keyword(s):  
Elliptic Equation ◽  
Kirchhoff Type

scholarly journals Blow-up solutions for a Kirchhoff type elliptic equation with trapping potential

2018 ◽  
Vol 17 (5) ◽  
pp. 1875-1897 ◽  
Author(s):  
Helin Guo ◽  
◽  
Yimin Zhang ◽  
Huansong Zhou ◽  
Keyword(s):  
Elliptic Equation ◽  
Blow Up ◽  
Trapping Potential ◽  
Kirchhoff Type

Another approach on an elliptic equation of Kirchhoff type

2013 ◽  
Vol 70 (1) ◽  
pp. 11-22
Author(s):  
Anderson Luis Albuquerque de Araujo
Keyword(s):  
Elliptic Equation ◽  
Kirchhoff Type

Positive solutions of Kirchhoff-type non-local elliptic equation: a bifurcation approach

2017 ◽  
Vol 147 (4) ◽  
pp. 875-894 ◽  
Author(s):  
Zhanping Liang ◽  
Fuyi Li ◽  
Junping Shi
Keyword(s):  
Elliptic Equation ◽  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Nonlinear Eigenvalue Problem ◽  
Global Bifurcation ◽  
Integral Term ◽  
Kirchhoff Type ◽  
Nonlinear Elliptic ◽  
Linear Eigenvalue Problem ◽  
Non Local

Positive solutions of a Kirchhoff-type nonlinear elliptic equation with a non-local integral term on a bounded domain in ℝN, N ⩾ 1, are studied by using bifurcation theory. The parameter regions of existence, non-existence and uniqueness of positive solutions are characterized by the eigenvalues of a linear eigenvalue problem and a nonlinear eigenvalue problem. Local and global bifurcation diagrams of positive solutions for various parameter regions are obtained.

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