Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity
@article{Ghergu2018ExactBA, title={Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity}, author={Marius Ghergu and Sunghan Kim and Henrik Shahgholian}, journal={Advances in Nonlinear Analysis}, year={2018}, volume={8}, pages={995 - 1003} }
Abstract We study the semilinear elliptic equation - Δ u = u α | log u | β in B 1 ∖ { 0 } , -\Delta u=u^{\alpha}\lvert\log u|^{\beta}\quad\text{in }B_{1}\setminus\{0\}, where B 1 ⊂ ℝ n {B_{1}\subset{\mathbb{R}}^{n}} , with n ≥ 3 {n\geq 3} , n n - 2 < α < n + 2 n - 2 {\frac{n}{n-2}<\alpha<\frac{n+2}{n-2}} and - ∞ < β < ∞ {-\infty<\beta<\infty} . Our main result establishes that the nonnegative solution u ∈ C 2 ( B 1 ∖ { 0 } ) {u\in C^{2}(B_{1}\setminus\{0\})} of the above equation either has…
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References
SHOWING 1-9 OF 9 REFERENCES
Maximum principles for the fractional p-Laplacian and symmetry of solutions
- MathematicsAdvances in Mathematics
- 2018
Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities
- Mathematics
- 2014
In this paper, we study the local behaviors of nonnegative local solutions of fractional order semi-linear equations $${(-\Delta )^\sigma u=u^{\frac{n+2\sigma}{n-2\sigma}}}$$(-Δ)σu=un+2σn-2σ with an…
Local asymptotic symmetry of singular solutions to nonlinear elliptic equations
- Mathematics
- 1996
A Assume that u is a solution to (1), and g(t) is a nonnegative locally Lipschitz function satgfying: (i) g(t) is nondecreasing in t for t > O. (ii) t-(n+2)g(tn--2 ) is nonincreasing Jor t > O, (iii)…
Asymptotic behavior of solutions to the σk-Yamabe equation near isolated singularities
- Mathematics
- 2010
Abstractσk-Yamabe equations are conformally invariant equations generalizing the classical Yamabe equation. In (J. Funct. Anal. 233: 380–425, 2006) YanYan Li proved that an admissible solution with…
Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
- Mathematics
- 1989
On etudie les solutions regulieres non negatives de l'equation conformement invariante −Δu=u (n+2)/(n−2) , u>0 dans une boule perforee, B 1 (0)\{0}⊂R n , n≥3, avec une singularite isolee a l'origine
Refined asymptotics for constant scalar curvature metrics with isolated singularities
- Mathematics
- 1999
Abstract. We consider the asymptotic behaviour of positive solutions u of the conformal scalar curvature equation, , in the neighbourhood of isolated singularities in the standard Euclidean ball.…
Global and local behavior of positive solutions of nonlinear elliptic equations, Comm
- Pure Appl. Math
- 1981