6 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}…
Normalized solutions for a class of fractional Choquard equations with the HLS lower critical term and a nonlocal perturbation
Shaoxiong Chen, Vishvesh Kumar, Zhipeng Yang +1
In this paper, we study the mass-constrained fractional Choquard equation \( (-Î)^s u = λu + α(I_μ* |u|^{\frac{2N-μ}{N}})|u|^{\frac{2N-μ}{N}-2}u + (I_μ* |u|^p)|u|^{p-2}u \)…
Multiple standing waves of Helmholtz equation with mixed dispersion concentrating in the high frequency limit
Shaoxiong Chen, Fei Yuan, Fukun Zhao +1
In this paper, we study the nonlinear Helmholtz equation with mixed dispersion \begin{equation*} Î^2 u-βk^2\, Îu+αk^4 u=W(x)\, |u|^{p-2}u~\text{in}~\mathbb{R}^N, \end{equation*…
Existence and concentration of ground state solutions for an exponentially critical Choquard equation involving mixed local-nonlocal operators
Shaoxiong Chen, Min Yang, Zhipeng Yang
We study the Choquard equation involving mixed local and nonlocal operators \[-\varepsilon^{2}Îu+\varepsilon^{2s}(-Î)^{s}u+V(x)u=\varepsilon^{μ-2}\left(\frac{1}{|x|^μ}*F(u)\rig…
Normalized solutions for a class of fractional Choquard equations with mixed nonlinearities
Shaoxiong Chen, Zhipeng Yang, Xi Zhang
In this paper we study the following fractional Choquard equation with mixed nonlinearities: \[ \left\{ \begin{array}{l} (-Î)^s u = λu + α\left( I_μ* |u|^q \right) |u|^{q-2} u…