This introduction to the singularly perturbed methods in the nonlinear elliptic partial
differential equations emphasises the existence and local uniqueness of solutions exhibiting …

We consider the following prescribed scalar curvature problem on SN where K˜ is positive
and rotationally symmetric. We show that if K˜ has a local maximum point between the poles …

We consider the boundary value problem Δu+ε^2k\left(x\right)e^u=0 in a bounded, smooth
domain Ω in R^2 with homogeneous Dirichlet boundary conditions. Here ε> 0, k (x) is a non …

In this paper, we study a class of critical Choquard equations with axisymmetric potentials,-Δ
u+ V (| x′|, x′′) u=(| x|-4∗| u| 2) u in R 6, where (x′, x′′)∈ R 2× R 4, V (| x′|, x′′) is …

This paper deals with the following nonlinear elliptic equation− Δ u+ V (| y′|, y ″) u= u N+ 2
N− 2, u> 0, u∈ H 1 (RN), where (y′, y ″)∈ R 2× RN− 2, V (| y′|, y ″) is a bounded non …

Green’s function and infinite-time bubbling in the critical nonlinear heat equation Page 1 DOI
10.4171/JEMS/922 J. Eur. Math. Soc. 22, 283–344 c European Mathematical Society 2020 …

In this paper, we consider the Caffarelli–Kohn–Nirenberg (CKN) inequality:(∫ RN| x|-b (p+
1)| u| p+ 1 dx) 2 p+ 1≤ C a, b, N∫ RN| x|-2 a|∇ u| 2 dx where N≥ 3, a< N-2 2, a≤ b≤ a+ 1 …

The main purpose of this paper is to construct families of positive solutions for the equation -
Δu=u^(N+2)/(N-2)+εu\qquadin\Omega,\u=0\qquad\qquad\qquad\qquad\qquadon\partialΩ …

We are interested in the existence and asymptotic behavior of the solutions of the following
critical Hartree equation with small parameter ε> 0,(0.1){− Δ u=(∫ Ω u 2 μ⁎(y)| x− y| μ dy) u 2 …

We consider the following semilinear elliptic equation with critical exponent: Δ u= K (x) u (n+
2)/(n-2), u> 0 in ℝ n, where n≥ 3, K> 0 is periodic in (x 1,…, xk) with 1≤ k<(n-2)/2. Under …