Results 61 to 70 of about 12,592 (145)
Advances in Nonlinear AnalysisThis article is devoted to studying the existence of positive solutions to the following fractional Choquard equation: (−Δ)su+u=∫Ω∣u(y)∣p∣x−y∣N−αdy∣u∣p−2u+ε∫Ω∣u(y)∣2α,s*∣x−y∣N−αdy∣u∣2α,s*−2u,inΩ,u=0,onRN\Ω,\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+u=
Ye Fumei, Yu Shubin, Tang Chun-Lei
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Conservation Science and Practice, Volume 7, Issue 8, August 2025.This article presents a lifecycle approach to providing artificial tree hollows for sustainable habitat restoration in response to human‐induced disturbances. It integrates biological and technological lifecycles to evaluate the long‐term consequences of material choices, construction methods, and design approaches.
Dan Parker +6 more
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Odd moments and adding fractions
Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.Abstract We prove near‐optimal upper bounds for the odd moments of the distribution of coprime residues in short intervals, confirming a conjecture of Montgomery and Vaughan. As an application, we prove near‐optimal upper bounds for the average of the refined singular series in the Hardy–Littlewood conjectures concerning the number of prime k$k$‐tuples
Thomas F. Bloom, Vivian Kuperberg
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Normalized solutions for the Choquard equations with critical nonlinearities
Advances in Nonlinear AnalysisThis study is concerned with the existence of normalized solutions for the Choquard equations with critical nonlinearities −Δu+λu=f(u)+(Iα∗∣u∣2α*)∣u∣2α*−2u,inRN,∫RN∣u∣2dx=a2,\left\{\begin{array}{l}-\Delta u+\lambda u=f\left(u)+\left({I}_{\alpha }\ast ...
Gao Qian, He Xiaoming
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The free boundary for semilinear problems with highly oscillating singular terms
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract We investigate general semilinear (obstacle‐like) problems of the form Δu=f(u)$\Delta u = f(u)$, where f(u)$f(u)$ has a singularity/jump at {u=0}$\lbrace u=0\rbrace$ giving rise to a free boundary. Unlike many works on such equations where f$f$ is approximately homogeneous near {u=0}$\lbrace u = 0\rbrace$, we work under assumptions allowing ...
Mark Allen +2 more
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Estimates for smooth Weyl sums on minor arcs
Bulletin of the London Mathematical Society, Volume 57, Issue 3, Page 657-668, March 2025.Abstract We provide new estimates for smooth Weyl sums on minor arcs and explore their consequences for the distribution of the fractional parts of αnk$\alpha n^k$. In particular, when k⩾6$k\geqslant 6$ and ρ(k)$\rho (k)$ is defined via the relation ρ(k)−1=k(logk+8.02113)$\rho (k)^{-1}=k(\log k+8.02113)$, then for all large numbers N$N$ there is an ...
Jörg Brüdern, Trevor D. Wooley
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Advanced Nonlinear StudiesThis paper investigates the existence and multiplicity of solutions to the following double critical p-fractional Schrödinger–Poisson system with electromagnetic fields in R3 ${\mathbb{R}}^{3}$ :ϵps−Δp,Aϵsu+V(x)|u|p−2u−ϕ|u|ps♯−2u=|u|ps*−2u+gx,|u|p|u|p−2u
He Xian, Liang Sihua, Pucci Patrizia
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Additive triples of bijections, or the toroidal semiqueens problem
, 2016 We prove an asymptotic for the number of additive triples of bijections $\{1,\dots,n\}\to\mathbb{Z}/n\mathbb{Z}$, that is, the number of pairs of bijections $\pi_1,\pi_2\colon \{1,\dots,n\}\to\mathbb{Z}/n\mathbb{Z}$ such that the pointwise sum $\pi_1 ...
Eberhard, Sean +2 more
core
Uniform Treatment of Integral Majorization Inequalities with Applications to Hermite-Hadamard-Fejér-Type Inequalities and f-Divergences. [PDF]
Entropy (Basel), 2023 Horváth L.
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