14 papers
A positive ground state for a planar Choquard equation with mixed diffusion and critical exponential growth
Shaoxiong Chen, Sekhar Ghosh, Vishvesh Kumar +1
We study a two-dimensional Choquard equation driven by the mixed local and nonlocal operator , where the nonlinearity has critical exponential growth of Trudinger--…
Existence of positive and sign-changing solutions for a Choquard equation involving mixed local and nonlocal operators
Shaoxiong Chen, Hichem Hajaiej, Min Yang +1
We study the Choquard equation involving mixed local and nonlocal operators \[ -Îu + (-Î)^{s}u + V(x)u = \left(\frac{1}{|x|^μ} * F(u)\right) f(u) \quad \text{in } \mathbb{R}^{2}…
Infinitely many sign-changing solutions for logarithmic Schrödinger equations via an \(L^p\)-perturbation approach
Chen Huang, Zhipeng Yang, Jiazheng Zhou
We study the logarithmic Schrödinger equation \[ -Îu+V(x)u=u\log u^2,\qquad x\in\mathbb R^N,\ N\ge3. \] Since the logarithmic energy is not \(C^1\) on the natural space \(H_V^1(\…
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, \[ (-Î)^s u = \left( \int_{\mathbb{R}^N\setminus\{0\}} \frac{u^p(y)}…
Higher-Order Heat Estimates and Semilinear Heat Equations on the Noncommutative Torus
Fulin Yang, Zhipeng Yang
We establish sharp higher-order heat estimates with complete bound on the noncommutative tori \(\mathbb{T}_θ^{n}\) and show the optimality in the small-time order. As an applicati…
On the existence of normalized solutions to a class of fractional Choquard equation with potentials
Yongpeng Chen, Zhipeng Yang, Jianjun Zhang
This paper investigates the existence of normalized solutions to the nonlinear fractional Choquard equation: $$ (-Î)^s u+V(x) u=λu+f(x)\left(I_α*\left(f|u|^q\right)\right)|u|^{q…