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- W2967971100 endingPage "111601" @default.
- W2967971100 startingPage "111601" @default.
- W2967971100 abstract "Consider the existence, nonexistence and global estimates of k-convex solutions to the boundary blow-up k-Hessian problem Sk(D2u(x))=H(x)[u(x)]k[lnu(x)]β>0forx∈Ω,u(x)→+∞asdist(x,∂Ω)→0. Here k∈{1,2,…,N}, Sk(D2u) is the k-Hessian operator, β>0, Ω is a smooth, bounded, strictly convex domain in RN(N≥2), and H(x) is a positive weight function which is singular near the boundary ∂Ω. We first give the existence and nonexistence results of k-convex solution to the above boundary blow-up problem on a larger range of H and β. Then we show that there is a k-convex solution provided that H(x) grows fast near ∂Ω and uk[lnu]β grows slow at ∞. It turns out that this case is more difficult to handle than the case in which H(x) grows slow near ∂Ω and uk[lnu]β grows fast at ∞. This needs some new ingredients in the arguments." @default.
- W2967971100 created "2019-08-22" @default.
- W2967971100 creator A5038988340 @default.
- W2967971100 creator A5069338467 @default.
- W2967971100 date "2020-01-01" @default.
- W2967971100 modified "2023-10-02" @default.
- W2967971100 title "On a<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e22 altimg=si26.svg><mml:mi>k</mml:mi></mml:math>-Hessian equation with a weakly superlinear nonlinearity and singular weights" @default.
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- W2967971100 doi "https://doi.org/10.1016/j.na.2019.111601" @default.
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