We consider Liouville-type and partial regularity results for the nonlinear fourth-order
problem Δ 2 u=| u| p− 1 u in R n, where p> 1 and n⩾ 1. We give a complete classification of …

We examine the elliptic system given by {equation}\label {system_abstract}-\Delta u= v^
p,\qquad-\Delta v= u^\theta,\qquad\{in}\IR^ N,{equation} for $1< p\le\theta $ and the fourth …

We examine the weighted Lane–Emden system {− Δ u=(1+| x| 2) α 2 vp,− Δ v=(1+| x| 2) α 2
uq, in RN, where 1< p≤ q and α> 0, and the weighted Lane–Emden equation− Δ u=(1+| x …

On stable solutions of the biharmonic problemwith polynomial growth Page 1 Pacific Journal of
Mathematics ON STABLE SOLUTIONS OF THE BIHARMONIC PROBLEM WITH POLYNOMIAL …

New embeddings of weighted Sobolev spaces are established. Using such embeddings, we
obtain the existence and regularity of positive solutions with Navier boundary value …

In this paper, we are concerned with the weighted elliptic system with the advection term
in\;\mathbb R^ N,-ω (x) Δ u (x)-∇ ω (x)·∇ u (x)= ω 1 v ϑ,-ω (x) Δ v (x)-∇ ω (x)·∇ v (x)= ω 2 …

Classification of Stable Solutions to a Non-Local Gelfand–Liouville Equation Page 1 A. Hyder and
W. Yang (2022) “Classification of Stable Solutions to a Non-Local Gelfand–Liouville Equation,” …

We study existence and stability properties of entire solutions of a polyharmonic equation
with an exponential nonlinearity. We study existence of radial entire solutions and we …

We examine the weighted elliptic system {− Δ u=(1+| x| 2) α 2 v,− Δ v=(1+| x| 2) α 2 up, in RN,
and prove Liouville type theorems for the classical positive and nonnegative stable solutions …

Regularity of the extremal solutions for the Liouville system Page 1 Regularity of the extremal
solutions for the Liouville system Louis Dupaigne, Alberto Farina and Boyan Sirakov Abstract …