We concern a family $\{(u_ {\varepsilon}, v_ {\varepsilon})\} _ {\varepsilon> 0} $ of solutions
of the Lane-Emden system on a smooth bounded convex domain $\Omega $ in $\mathbb …

We address the solvability of the critical Lane-Emden system in a smooth bounded domain
with a small spherical hole of radius ϵ> 0. We prove that the system admits a family of …

We study the following Lane–Emden system: with a bounded regular domain of,, and
exponents belonging to the so-called critical hyperbola. We show that, under suitable …

We study existence and convergence properties of least-energy symmetric solutions (less)
to the pure critical exponent problem (-Δ) s⁢ us=| us| 2 s⋆-2⁢ us, us∈ D 0 s⁢(Ω), 2 s⋆:= 2⁢ …

In this paper, we prove the second-order Sobolev inequalities on Cayley graphs of groups of
polynomial growth. We use the discrete Concentration-Compactness principle to prove the …

Let (M, g) be a smooth compact Riemannian manifold of dimension N≥ 8. We are
concerned with the following elliptic system-Δ gu+ h (x) u= vp-α ε, in M,-Δ gv+ h (x) v= uq-β ε …

In this paper, we study the following Lane-Emden system with nearly critical non-power
nonlinearity\begin {eqnarray*}\left\{\arraycolsep= 1.5 pt\begin {array}{lll}-\Delta u=\frac …

This paper establishes a dual variational framework for studying the existence and
multiplicity of solutions to a class of Helmholtz systems. We first focus on a compact …

Let $(\mathcal {M}, g) $ and $(\mathcal {K},\kappa) $ be two Riemannian manifolds of
dimensions $ N $ and $ m $, respectively. Let $\omega\in C^ 2 (\mathcal {M}) $, $\omega> …

In this paper, we consider the critical Lane-Emden system\begin {align*}\begin {cases}-
\Delta u= K_1 (y) v^ p,\quad y\in\mathbb {R}^ N, &\\-\Delta v= K_2 (y) u^ q,\quad y\in\mathbb …