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Uniqueness of Single Peak Solutions for a Kirchhoff Equation
MathematicsWe deal with the following singular perturbation Kirchhoff equation: −ϵ2a+ϵb∫R3|∇u|2dyΔu+Q(y)u=|u|p−1u,u∈H1(R3), where constants a,b,ϵ>0 and ...
Junhao Lv, Shichao Yi, Bo Sun
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Multi-peak Solutions for a Singularly Perturbed Semilinear Elliptic Problem
Journal of Differential Equations, 2000 The existence of single (multi)-peak positive solutions of the Dirichlet problem for the equation \(-\varepsilon^2\Delta u+ u= u^{p-1}\), when \(\varepsilon\downarrow 0\), in a bounded smooth domain \(\Omega\subset\mathbb{R}^N\), for \(p\in (2;2N/(N- 2))\) if \(N\geq 3\) and \(p\in (2;\infty)\) if \(N= 2\), depends on the topology of \(\Omega\).
Daomin Cao, Ezzat S Noussair
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Peak solutions for the fractional Nirenberg problem [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2015 In this paper, the fractional order curvature equation $(-Δ)^γu = (1 + \varepsilon K(x))u^{\frac{N + 2γ}{N - 2γ}}$ in $\mathbb{R}^N$ is considered. Assuming $K(x)$ has two critical points satisfying certain local conditions, we prove the existence of two-peak solutions.
Youquan Zheng
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Non-Degeneracy of Peak Solutions to the Schrödinger–Newton System
Advanced Nonlinear Studies, 2021 We are concerned with the following Schrödinger–Newton problem:
Guo Qing, Xie Huafei
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Interior Peak Solutions for a Semilinear Dirichlet Problem
AxiomsIn this paper, we consider the semilinear Dirichlet problem (Pε):−Δu+V(x)u=un+2n−2−ε, u>0 in Ω, u=0 on ∂Ω, where Ω is a bounded regular domain in Rn, n≥4, ε is a small positive parameter, and V is a non-constant positive C2-function on Ω¯.
Hissah Alharbi +3 more
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Sign-changing two-peak solutions for an elliptic free boundary problem related to confined plasmas
Advances in Nonlinear Analysis, 2018 By a perturbative argument, we construct solutions for a plasma-type problem with two opposite-signed sharp peaks at levels 1 and -γ{-\gamma}, respectively, where ...
Pisante Giovanni, Ricciardi Tonia
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Existence of normalized peak solutions for a coupled nonlinear Schrödinger system
Advances in Nonlinear AnalysisIn this article, we study the following nonlinear Schrödinger system −Δu1+V1(x)u1=αu1u2+μu1,x∈R4,−Δu2+V2(x)u2=α2u12+βu22+μu2,x∈R4,\left\{\begin{array}{ll}-\Delta {u}_{1}+{V}_{1}\left(x){u}_{1}=\alpha {u}_{1}{u}_{2}+\mu {u}_{1},& x\in {{\mathbb{R}}}^{4},\\
Yang Jing
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Solutions with peaks for a coagulation-fragmentation equation. Part II: Aggregation in peaks [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2021 The aim of this two-part paper is to investigate the stability properties of a special class of solutions to a coagulation-fragmentation equation. We assume that the coagulation kernel is close to the diagonal kernel, and that the fragmentation kernel is diagonal.
Marco Bonacini +2 more
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Index-Based Solutions for Efficient Density Peak Clustering [PDF]
IEEE Transactions on Knowledge and Data Engineering, 2022 Density Peak Clustering (DPC), a popular density-based clustering approach, has received considerable attention from the research community primarily due to its simplicity and fewer-parameter requirement. However, the resultant clusters obtained using DPC are influenced by the sensitive parameter $d_c$, which depends on data distribution and ...
Zafaryab Rasool +4 more
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Journal of Cannabis Research, 2021 Background This study describes the design, optimization, and stress-testing of a novel phytocannabinoid nanoemulsion generated using high-pressure homogenization.
Abhinandan Banerjee +3 more
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