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On the stability of the Caffarelli–Kohn–Nirenberg inequality
In this paper, we consider the Caffarelli–Kohn–Nirenberg (CKN) inequality: $$\begin{aligned} \bigg (\int _{{\mathbb {R}}^N}|x|^{-b(p+1)}|u|^{p...
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Local uniqueness of the magnetic Ginzburg–Landau equation
In this paper, we consider the magnetic Ginzburg–Landau equation: $$\begin{aligned} \left\{ \begin{aligned}-\Delta _A \psi +\frac{\lambda }{2}(|\psi |^2-1)\psi =0\quad \text {in }{\mathbb {R}}^2,\\ \nabla \times...
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Spikes of the two-component elliptic system in \({\mathbb {R}}^4\) with the critical Sobolev exponent
Consider the following elliptic system: $$\begin{aligned} \left\{ \begin{aligned}&-\varepsilon ^2\Delta u_1+\lambda _1u_1=\mu _1u_1^3+...
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On the semiclassical solutions of a two-component elliptic system in \(\mathbb {R}^4\) with trap** potentials and Sobolev critical exponent: the repulsive case
Consider the following elliptic system: $$\begin{aligned} \left\{ \begin{array}{ll} -\varepsilon ^2\Delta u_1+V_1(x)u_1=\mu _1u_1^3+\a...
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On a K-component elliptic system with the Sobolev critical exponent in high dimensions: the repulsive case
Study the following K-component elliptic system Here $$k\g...
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On a two-component Bose–Einstein condensate with steep potential wells
In this paper, we study the following two-component systems of nonlinear Schrödinger equations $$\begin{aligned} \left\{ \begin{array}...
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Existence of nontrivial solution for Schrödinger–Poisson systems with indefinite steep potential well
In this paper, we study a class of nonlinear Schrödinger–Poisson systems with indefinite steep potential well: $$\begin{aligned} \left...
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Open AccessInfinitely many sign-changing solutions for p-Laplacian equation involving the critical Sobolev exponent
In this paper, we study the following problem:
