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Asymptotic behaviors of solutions to quasilinear elliptic equations with critical Sobolev growth and Hardy potential
Abstract Optimal estimates on the asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations − Δ p u − μ | x | p | u |Expand
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Uniqueness and nondegeneracy of ground states for Choquard equations in three dimensions
We obtain uniqueness and nondegeneracy results for ground states of Choquard equations $$-\Delta u+u=\left( |x|^{-1}*|u|^{p}\right) |u|^{p-2}u$$-Δu+u=|x|-1∗|u|p|u|p-2u in $$\mathbb {R}^{3}$$R3,Expand
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Uniqueness and Nondegeneracy of positive solutions to Kirchhoff equations and its applications in singular perturbation problems
In the present paper, we establish the uniqueness and nondegeneracy of positive energy solutions to the Kirchhoff equation \begin{eqnarray*} -\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)\DeltaExpand
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Nondegeneracy of positive solutions to a Kirchhoff problem with critical Sobolev growth
TLDR
We prove uniqueness and nondegeneracy of positive solutions to the following Kirchhoff equations with critical growth − a + b ∫ R 3 . Expand
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Non-invasive genetic analysis indicates low population connectivity in vulnerable Chinese gorals: concerns for segregated population management
Detailed information on the size and genetic structure of wildlife populations is critical for developing effective conservation strategies, especially for those species that have suffered populationExpand
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Remarks on Nondegeneracy of Ground States for Quasilinear Schr\"odinger Equations
In this paper, we answer affirmatively the problem proposed by A. Selvitella in his paper "Nondegenracy of the ground state for quasilinear Schr\"odinger Equations" (see Calc. Var. Partial Differ.Expand
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A singularly perturbed Kirchhoff problem revisited
Abstract In this paper, we revisit the singularly perturbation problem (0.1) − ( ϵ 2 a + ϵ b ∫ R 3 | ∇ u | 2 ) Δ u + V ( x ) u = | u | p − 1 u in  R 3 , where a , b , ϵ > 0 , 1 p 5 are constants andExpand
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GRADIENT ESTIMATES FOR SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS WITH CRITICAL SOBOLEV GROWTH AND HARDY POTENTIAL
This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\,Expand
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Local uniqueness of multi-peak solutions to a class of Kirchhoff equations
where ǫ > 0 is a parameter, V : R → R is a bounded continuous function. Under some mild conditions on V , Luo, Peng, Wang and the last named author of the present paper [22] proved the existence ofExpand