" The book describes how functional inequalities are often manifestations of natural
mathematical structures and physical phenomena, and how a few general principles …

In this survey paper, we consider variational problems involving the Hardy–Schrödinger
operator L_ γ:=-Δ-γ| x|^ 2 L γ:=-Δ-γ| x| 2 on a smooth domain Ω Ω of R^ n R n with 0 ∈ Ω 0∈ …

We study the following system of nonlinear Schrödinger equations: where N⩾ 3, 2⁎= 2NN−
2, 1< p< 2⁎− 1 and μ, ν, λ are positive parameters satisfying 0< λ< μν. We show that, there is …

In this paper, we study the positive radial solutions for the Hénon equations with weighted
critical exponents on the unit ball BB in ℝ NR^ N with N⩾ 3 N\geqslant 3. We first confirm …

We study the following elliptic system with critical exponent: Here, Ω is a smooth bounded
domain of ℝ N (N≥ 6), is the critical Sobolev exponent, 0< λ1, λ2< λ1 (Ω) and μ1, μ2> 0 …

In this article, we establish the weighted Trudinger–Moser inequality of the scaling invariant
form including its best constant and prove the existence of a maximizer for the associated …

In this paper, we consider the following PDE involving two Sobolev–Hardy critical
exponents, 0.1\left {& Δ u+ λ u^ 2^*(s_1)-1| x|^ s_1+ u^ 2^*(s_2)-1| x|^ s_2= 0\quad in …

Let Ω Ω be a C^ 1 C 1 open bounded domain in R^ N,\, N ≥ 3, RN, N≥ 3, with 0 ∈ ̄ Ω. 0∈
Ω¯. We consider the following problem involving Hardy–Sobolev critical …

In this paper, we investigate the existence of multiple positive solutions to the following multi-
critical elliptic problem 0.1-Δ u= λ| u| p-2 u+∑ i= 1 k (| x|-(N-α i)∗| u| 2 i∗)| u| 2 i∗-2 u in Ω …

We consider the following problem where $${\mu\ge 0, 0 &lt; s &lt; 2, 0\in\partial\Omega} $$
and Ω is a bounded domain in R. We prove that if $${N\ge 7, a (0) &gt; 0} $$ and all the …