Boundary blow-up solutions to the k-Hessian equation with the logarithmic nonlinearity and singular weights

2022 ◽  
Vol 24 (1) ◽  
Author(s):  
Xinqiu Zhang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Blow Up ◽  
Hessian Equation ◽  
Singular Weights

Boundary blow-up solutions to the k-Hessian equation with singular weights

2021 ◽  
Vol 116 ◽  
pp. 106964
Author(s):  
Xinqiu Zhang ◽  
Lishan Liu
Keyword(s):  
Blow Up ◽  
Hessian Equation ◽  
Singular Weights

Boundary blow-up solutions to thek-Hessian equation with singular weights

2018 ◽  
Vol 167 ◽  
pp. 51-66 ◽  
Author(s):  
Xuemei Zhang ◽  
Meiqiang Feng
Keyword(s):  
Blow Up ◽  
Hessian Equation ◽  
Singular Weights

scholarly journals A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Xinguang Zhang ◽  
Lishan Liu ◽  
Yonghong Wu ◽  
Yujun Cui
Keyword(s):  
Nonlinear Operator ◽  
Blow Up ◽  
Growth Conditions ◽  
Necessary Condition ◽  
Radial Solutions ◽  
Hessian Equation ◽  
Nonexistence And Existence ◽  
Sufficient And Necessary Condition

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained. 

Boundary blow-up elliptic problems with nonlinear gradient terms and singular weights

2008 ◽  
Vol 138 (6) ◽  
pp. 1403-1424 ◽  
Author(s):  
Zhijun Zhang
Keyword(s):  
Regular Variation ◽  
Blow Up ◽  
Smooth Boundary ◽  
Elliptic Problems ◽  
Variation Theory ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Comparison Functions ◽  
Positive Index ◽  
Singular Weights

By Karamata regular variation theory, a perturbation method and construction of comparison functions, we show the exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems Δu ± |Δu|q = b(x)g(u), u > 0 in Ω, u|∂Ω = ∞, where Ω is a bounded domain with smooth boundary in ℝN, q > 0, g ∈ C1[0, ∞) is increasing on [0, ∞), g(0) = 0, g′ is regularly varying at infinity with positive index ρ and b is non-negative in Ω and is singular on the boundary.

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