6 papers · 1 filter
Symmetry and Monotonicity for Subcritical Fractional Hartree Equations with Singular Sets of Zero Capacity
Guangze Gu, Aleks Jevnikar, Zhipeng Yang
We study positive weak singular solutions of the subcritical fractional Hartree equation \[ (-Δ)^s u = \left( \int_{\mathbb{R}^N\setminusΓ} \frac{u^p(y)}{|x-y|^μ}d y \right)u^q \qu…
Isolated Singularities for Fractional Hartree Equations
Guangze Gu, Aleks Jevnikar, Zhipeng Yang
We study isolated singularities of positive solutions to a fractional Hartree equation with Riesz interaction, \[ (-Δ)^s u = \left( \int_{\mathbb{R}^N\setminus\{0\}} \frac{u^p(y)}{…
Qualitative bifurcation diagram for Grad-Shafranov type equations
Daniele Bartolucci, Guangze Gu, Aleks Jevnikar +2
We study the qualitative behavior of solutions of Grad-Shafranov type equations arising in plasma physics with general differential operators and general nonlinearities. In particu…
On nonlinear elliptic problems with Hardy-Littlewood-Sobolev critical exponent and Sobolev-Hardy critical exponent
Guangze Gu, Aleks Jevnikar
In this paper we use variational methods to establish the existence of solutions for a class of nonlinear elliptic problems involving a combined convolution-type and Hardy nonlinea…
Nonlocal problems with Hardy-Littlewood-Sobolev critical exponent and Hardy potential
Guangze Gu, Aleks Jevnikar
We are concerned with a Brezis-Nirenberg type problem for a critical Choquard equation, in the sense of Hardy-Littlewood-Sobolev inequality, and with the Hardy potential in a smoot…
Symmetry and monotonicity of singular solutions for the Hartree equation
Ying Cai, Guangze Gu, Aleks Jevnikar
In this paper we are concerned with positive singular solutions of the following nonlocal Hartree equation $$-Δu\!=\Big( \int_{\mathbb{R}^N\setminus Γ}\frac{F(u(y))}{|x-y|^μ}dy \Bi…