Results 1 to 10 of about 89 (75)
Transactions of the London Mathematical Society, 2021 In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non‐linearities on an unbounded domain, and show that such an equation with positive or sign‐changing weight potentials admits at least one positive ...
Haining Fan, Zhaosheng Feng, Xingjie Yan
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From Hardy to Rellich inequalities on graphs
Proceedings of the London Mathematical Society, Volume 122, Issue 3, Page 458-477, March 2021., 2021 Abstract We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality.
Matthias Keller +2 more
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Advanced Nonlinear Studies, 2023 We consider the existence and nonexistence of the positive solution for the following Brézis-Nirenberg problem with logarithmic perturbation: −Δu=∣u∣2∗−2u+λu+μulogu2x∈Ω,u=0x∈∂Ω,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{ll}-\Delta u={| u| }^{{2}^
Deng Yinbin +3 more
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Positive solution for a nonlocal problem with strong singular nonlinearity
Open Mathematics, 2023 In this article, we consider a nonlocal problem with a strong singular term and a general weight function. By using Ekeland’s variational principle, we prove a necessary and sufficient condition for the existence of a positive solution.
Wang Yue +3 more
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Advances in Nonlinear Analysis, 2022 In this paper we study the existence and the nonexistence of solutions to an inhomogeneous non-linear elliptic problem (P)−Δu+u=F(u)+κμ in RN, u>0 in RN, u(x)→0 as |x|→∞,- \Delta u + u = F(u) + \kappa \mu \quad {\kern 1pt} {\rm in}{\kern 1pt ...
Ishige Kazuhiro +2 more
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Monotonicity of solutions for fractional p-equations with a gradient term
Open Mathematics, 2022 In this paper, we consider the following fractional pp-equation with a gradient term: (−Δ)psu(x)=f(x,u(x),∇u(x)).{\left(-\Delta )}_{p}^{s}u\left(x)=f\left(x,u\left(x),\nabla u\left(x)). We first prove the uniqueness and monotonicity of positive solutions
Wang Pengyan
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Sign changing solutions of Poisson's equation
Proceedings of the London Mathematical Society, Volume 121, Issue 3, Page 513-536, September 2020., 2020 Abstract Let Ω be an open, possibly unbounded, set in Euclidean space Rm with boundary ∂Ω, let A be a measurable subset of Ω with measure |A| and let γ∈(0,1). We investigate whether the solution vΩ,A,γ of −Δv=γ1Ω∖A−(1−γ)1A with v=0 on ∂Ω changes sign. Bounds are obtained for |A| in terms of geometric characteristics of Ω (bottom of the spectrum of the ...
M. van den Berg, D. Bucur
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Open Mathematics, 2021 In this study, we consider the following quasilinear Choquard equation with singularity −Δu+V(x)u−uΔu2+λ(Iα∗∣u∣p)∣u∣p−2u=K(x)u−γ,x∈RN,u>0,x∈RN,\left\{\begin{array}{ll}-\Delta u+V\left(x)u-u\Delta {u}^{2}+\lambda \left({I}_{\alpha }\ast | u{| }^{p})| u{| }
Shao Liuyang, Wang Yingmin
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On a fractional Schrödinger-Poisson system with strong singularity
Open Mathematics, 2021 We investigate a fractional Schrödinger-Poisson system with strong singularity as follows: (−Δ)su+V(x)u+λϕu=f(x)u−γ,x∈R3,(−Δ)tϕ=u2,x∈R3,u>0,x∈R3,\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+V\left(x)u+\lambda \phi u=f\left(x){u}^{-\gamma },& x\in ...
Yu Shengbin, Chen Jianqing
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Open Mathematics, 2019 The present study is concerned with the following Schrödinger-Poisson system involving critical nonlocal ...
Shao Liuyang
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