If we had to formulate in one sentence what this book is about, it might be “How partial
differential equations can help to understand heat explosion, tumor growth or evolution of …

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

In this paper, we prove that any solution of the energy-critical wave equation in space
dimensions 3, 4 or 5, which is bounded in the energy space decouples asymptotically, for a …

Mathematical Analysis. – An overview on extremals and critical points of the Sobolev inequality
in convex cones, by Alberto Ro Page 1 Rend. Lincei Mat. Appl. 33 (2022), 967–995 DOI …

We consider the following prescribed scalar curvature equations in RN (0.1)− Δ u= K (| y|) u
2⁎− 1, u> 0 in RN, u∈ D 1, 2 (RN), where K (r) is a positive function, 2⁎= 2 NN− 2. We first …

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 …

We study the saddle type nodal solutions for the Choquard equation-Δ u=(I_ α*| u|^ N+ α N-
2)| u|^ N+ α N-2-2 u\quad in R^ N,-Δ u=(I α∗| u| N+ α N-2)| u| N+ α N-2-2 u in RN, where N ≥ …

We mainly show the nondegeneracy of positive bubble solutions for generalized energy-
critical Hartree equations (NLH)\begin {equation*}-{\Delta u}\sts {x}-{\bm\alpha}\sts …

The book offers an expanded version of lectures given at ETH Zürich in the framework of a
Nachdiplomvorlesung. Compactness and stability for nonlinear elliptic equations in the …

We construct a new family of entire solutions to the Yamabe equation− Δ u= n (n− 2) 4| u| 4
n− 2 u in D 1, 2 (R n). If n= 3 our solutions have maximal rank, being the first example in odd …