Results 41 to 50 of about 523 (145)
Existence of solutions to Schrödinger systems on locally finite graphs
Electronic Research ArchiveWe consider the existence of solutions for some Schrödinger systems on locally finite graphs. Using variationial method and Nehari manifold method, the existence and multiplicity of nontrivial solutions are proved.
Yan-Hong Chen, Hua Zhang
doaj +1 more source
The Nehari manifold for fractional systems involving critical nonlinearities
Communications on Pure and Applied Analysis, 2016 To appear in Commun.
He, X., Squassina, Marco, Zou, W.
openaire +5 more sources
The Nehari manifold for a boundary value problem involving Riemann–Liouville fractional derivative [PDF]
Advances in Difference Equations, 2018 Nuestro objetivo es investigar los siguientes problemas de valores límite no lineales de ecuaciones diferenciales fraccionarias: $$\begin{aligned} (\mathrm{P}_{\lambda})\ left\ {\ textstyle\begin {array} {l} -_{t} D_{1} ^{\alpha} ( \vert {}_{0} D_{t} ^{\alpha}(u(t)) \vert ^{p-2} {}_{0} D_{t} ^{\alpha}u(t) )\ \\\quad=f(t,u (t)) +\lambda g (t) \vert u(t)\
Kamel Saoudi +4 more
openaire +3 more sources
Fractional Q$Q$‐curvature on the sphere and optimal partitions
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional Q$Q$‐curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new
Héctor A. Chang‐Lara +2 more
wiley +1 more source
Superlinear perturbations of a double‐phase eigenvalue problem
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract We consider a perturbed version of an eigenvalue problem for the double‐phase operator. The perturbation is superlinear, but need not satisfy the Ambrosetti–Robinowitz condition. Working on the Sobolev–Orlicz space W01,η(Ω)$ W^{1,\eta }_{0}(\Omega)$ with η(z,t)=α(z)tp+tq$ \eta (z,t)=\alpha (z)t^{p}+t^{q}$ for 1
Yunru Bai +2 more
wiley +1 more source
Journal of Function Spaces, 2020 In this paper, we prove the existence and multiplicity of positive solutions for a class of fractional p & q Laplacian problem with singular nonlinearity.
Dandan Yang, Chuanzhi Bai
doaj +1 more source
Mathematical Modelling and Analysis, 2020 In this paper, we deal with a class of fractional Laplacian system with critical Sobolev-Hardy exponents and sign-changing weight functions in a bounded domain.
Jinguo Zhang, Tsing-San Hsu
doaj +1 more source
Normalized solutions of the critical Schrödinger–Bopp–Podolsky system with logarithmic nonlinearity
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract In this paper, we study the following critical Schrödinger–Bopp–Podolsky system driven by the p$p$‐Laplace operator and a logarithmic nonlinearity: −Δpu+V(εx)|u|p−2u+κϕu=λ|u|p−2u+ϑ|u|p−2ulog|u|p+|u|p*−2uinR3,−Δϕ+a2Δ2ϕ=4π2u2inR3.$$\begin{equation*} {\begin{cases} -\Delta _p u+\mathcal {V}(\varepsilon x)|u|^{p-2}u+\kappa \phi u=\lambda |u|^{p-2 ...
Sihua Liang +3 more
wiley +1 more source
Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco +3 more
wiley +1 more source
Planar Choquard equations with critical exponential reaction and Neumann boundary condition
Mathematische Nachrichten, Volume 297, Issue 10, Page 3847-3869, October 2024.Abstract We study the existence of positive weak solutions for the following problem: −Δu+α(x)u=∫ΩF(y,u)|x−y|μ1dyf(x,u)inΩ,∂u∂η+βu=∫∂ΩG(y,u)|x−y|μ2dνg(x,u)on∂Ω,$$\begin{equation*} \begin{aligned} \hspace*{65pt}-\Delta u + \alpha (x) u &= {\left(\int \limits _{\Omega }\frac{F(y,u)}{|x-y|^{{\mu _1}}}\;dy\right)}f(x,u) \;\;\text{in} \; \Omega,\\ \hspace ...
Sushmita Rawat +2 more
wiley +1 more source