Results 41 to 50 of about 628 (105)

Existence, symmetry, and regularity of ground states of a nonlinear Choquard equation in the hyperbolic space

Advances in Nonlinear Analysis
In this study, we explore the positive solutions of a nonlinear Choquard equation involving the Green kernel of the fractional operator (−ΔBN)−α⁄2{\left(-{\Delta }_{{{\mathbb{B}}}^{N}})}^{-\alpha /2} in the hyperbolic space, where ΔBN{\Delta }_{{{\mathbb{
Gupta Diksha, Sreenadh Konijeti
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Positive Ground State Solutions for Fractional (p, q)-Laplacian Choquard Equation with Singularity and Upper Critical Exponent

Fractal and Fractional
We prove the existence of a positive ground state solution for a fractional (p,q)-Laplacian Choquard equation that features both a singularity and an upper critical exponent.
Zhenyu Bai, Chuanzhi Bai
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Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth

Advances in Nonlinear Analysis
We study the following fractional Kirchhoff-Choquard equation: a+b∫RN(−Δ)s2u2dx(−Δ)su+V(x)u=(Iμ*F(u))f(u),x∈RN,u∈Hs(RN),\left\{\begin{array}{l}\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{\left|{\left(-\Delta )}^{\frac{s}{2}}u\right|}
Yang Jie, Chen Haibo
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Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

Boundary Value Problems, 2018
By using an abstract critical point theorem based on a pseudo-index related to the cohomological index, we prove the bifurcation results for the critical Choquard problems involving fractional p-Laplacian operator: (−Δ)psu=λ|u|p−2u+(∫Ω|u|pμ,s∗|x−y|μdy)|u|
Yuling Wang, Yang Yang
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Ground states for the pseudo-relativistic Hartree equation with external potential

, 2014
We prove existence of positive ground state solutions to the pseudo-relativistic Schr\"{o}dinger equation \begin{equation*} \left\{ \begin{array}{l} \sqrt{-\Delta +m^2} u +Vu = \left( W * |u|^{\theta} \right)|u|^{\theta -2} u \quad\text{in $\mathbb{R}^N$}
Cingolani, Silvia, Secchi, Simone
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Fractional Choquard Equations with Confining Potential With or Without Subcritical Perturbations

Advanced Nonlinear Studies, 2019
Abstract In this paper, we consider fractional Choquard equations with confining potentials. First, we show that they admit a positive ground state and infinitely many bound states. Then we prove the existence of two signed solutions when a superlinear and subcritical perturbation is added; in this case, the main feature is that such a ...
Dimitri Mugnai, Edoardo Proietti Lippi
openaire   +2 more sources

Nonlocal Kirchhoff superlinear equations with indefinite nonlinearity and lack of compactness

, 2019
We study the following Kirchhoff equation $$- \left(1 + b \int_{\mathbb{R}^3} |\nabla u|^2 dx \right) \Delta u + V(x) u = f(x,u), \ x \in \mathbb{R}^3.$$ A special feature of this paper is that the nonlinearity $f$ and the potential $V$ are indefinite ...
Li, Lin, Repovš, Dušan D., Rădulescu, Vicenţiu D.   +2 more
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Nonlocal Pertubations of Fractional Choquard Equation

, 2017
17 ...
openaire   +2 more sources

Multiplicity and concentration results for some nonlinear Schr\"odinger equations with the fractional $p$-Laplacian

, 2018
We consider a class of parametric Schr\"odinger equations driven by the fractional $p$-Laplacian operator and involving continuous positive potentials and nonlinearities with subcritical or critical growth.
Ambrosio, Vincenzo, Isernia, Teresa
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Concentration phenomena for anisotropic fractional Choquard equations and potential competition

Bulletin of Mathematical Sciences
In this paper, we study the existence of a weak solution to the following anisotropic fractional Choquard equation in [Formula: see text] as follows: ∑i=1m(−Δ)pisv+∑i=1mV(ζx)|v|pi−2v=λ1|x|μ∗Q(ζy)F(v)Q(ζx)𝔣(v)+(v+)qs∗−2v+,v+(x)=max{v(x),0}, where [Formula:
Trang Quynh Pham, Thin Van Nguyen
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