Results 31 to 40 of about 628 (105)

Existence Results for Fractional Choquard Equations with Critical or Supercritical Growth

Journal of Nonlinear Mathematical Physics, 2022
AbstractIn this paper, we study the following fractional Choquard equation with critical or supercritical growth $$\begin{aligned} \ (-\Delta )^su+V(x)u=f(x,u)+\lambda \left[ |x|^{-\mu }*|u|^p\right] p|u|^{p-2}u, \quad x \in {\mathbb {R}}^N, \end{aligned}$$
Dongpo Hu, Zhaowen Zheng, Ming Liu
openaire   +1 more source

Solutions with prescribed mass for a critical Choquard equation driven by a local-nonlocal operator [PDF]

Opuscula Mathematica
In this paper, we study the normalized solutions of the following critical growth Choquard equation with mixed local and nonlocal operators: \[\begin{split}-\Delta u +(-\Delta)^s u &= \lambda u +\mu |u|^{p-2}u +(I_{\alpha}*|u|^{2^*_{\alpha}})|u|^{2^*_ ...
Nidhi Nidhi, Konijeti Sreenadh
doaj   +1 more source

The semirelativistic Choquard equation with a local nonlinear term

, 2018
We propose an existence result for the semirelativistic Choquard equation with a local nonlinearity in $\mathbb{R}^N$ \begin{equation*} \sqrt{\strut -\Delta + m^2} u - mu + V(x)u = \left( \int_{\mathbb{R}^N} \frac{|u(y)|^p}{|x-y|^{N-\alpha}} \, dy \right)
Bieganowski, Bartosz, Secchi, Simone
core   +1 more source

Regularity and Classification of Solutions to Fractional‐Order Systems With Hartree‐Type Nonlinearities

Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.
This paper is concerned with the positive solutions to a fractional‐order system with Hartree‐type nonlinearity and its equivalent integral system. We firstly use the regularity lifting lemma to obtain the integrability and smoothness of the solutions.
Yu-Cheng An, Guai-Qi Tian, Douglas R. Anderson   +2 more
wiley   +1 more source

Solutions to upper critical fractional Choquard equations with potential

Advances in Differential Equations, 2020
In this paper, the upper critical fractional Choquard equation is considered. The interest in studying such equation comes from its strong connections with mathematical physics, for example, the fractional quantum mechanics, the Lévy random walk models, and the dynamics of pseudo-relativistic boson stars.
Li, Xinfu, Ma, Shiwang, Zhang, Guang
openaire   +2 more sources

On doubly nonlocal $p$-fractional coupled elliptic system

, 2017
\noi We study the following nonlinear system with perturbations involving p-fractional Laplacian \begin{equation*} (P)\left\{ \begin{split} (-\De)^s_p u+ a_1(x)u|u|^{p-2} &= \alpha(|x|^{-\mu}*|u|^q)|u|^{q-2}u+ \beta (|x|^{-\mu}*|v|^q)|u|^{q-2}u+ f_1(x)\;
Mukherjee, T., Sreenadh, K.
core   +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, Vicenţiu D. Rădulescu, K. Sreenadh   +2 more
wiley   +1 more source

Multiple Normalized Solutions to a Choquard Equation Involving Fractional p-Laplacian in ℝ^N

Fractal and Fractional
In this paper, we study the existence of multiple normalized solutions for a Choquard equation involving fractional p-Laplacian in RN. With the help of variational methods, minimization techniques, and the Lusternik–Schnirelmann category, the existence ...
Xin Zhang, Sihua Liang
doaj   +1 more source

Semiclassical analysis for pseudo-relativistic Hartree equations

, 2015
In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation $\sqrt{-\varepsilon^2 \Delta + m^2}u + V u = (I_\alpha * |u|^{p}) |u|^{p-2}u$ in $\mathbb{R}^N$ where $m>0$, $2 \leq p < \frac{2N}{N-1}$, $V \colon \mathbb{R}^N
Cingolani, Silvia, Secchi, Simone
core   +1 more source

Existence of Multiple Solutions for Certain Quasilinear Elliptic Problems Under Flux Boundary Conditions

Journal of Mathematics, Volume 2024, Issue 1, 2024.
In this paper, we consider the following quasilinear p⟶⋅‐elliptic problems with flux boundary conditions of the type −∑i=1N∂/∂xiaix,∂u/∂xi+bxupMx−2u=f1x,u−sgnug1x in Ω,∑i=1Naix,∂u/∂xiνi=cxuqx−2u+f2x,u−sgnug2x on ∂Ω.. Using the Fountain theorem and dual Fountain theorem, we prove the existence and multiplicity of solutions for a given problem, subject ...
Ahmed Ahmed, Taghi Ahmedatt, Yongqiang Fu   +2 more
wiley   +1 more source