Micro-and nanoelectromechanical systems (MEMS and NEMS), which combine electronics
with miniature-size mechanical devices, are essential components of modern technology. It …

Stable solutions of − u = f (u) in R Page 1 DOI 10.4171/JEMS/217 J. Eur. Math. Soc. 12, 855–882
c European Mathematical Society 2010 L. Dupaigne · A. Farina Stable solutions of − u = f (u) …

We are interested in the existence versus non-existence of non-trivial stable sub-and super-
solutions of\begin {equation}-\operatorname {div}(\omega _1\nabla u)=\omega _2 f …

We consider the boundary value problem {− div< sub> G(w< sub> 1∇< sub> G u)= w< sub>
2 f (u) in Ω, u= 0 on∂ Ω, where Ω is a bounded or unbounded C< sup> 1 domain of R< sup> …

We prove a Liouville type theorem for stable solutions of the equation− div (| D u| p− 2 D u)=
f (u) in the whole space RN, where f is a non-negative, non-decreasing and convex function …

We examine the equation given by (1)− Δ u+ a (x)⋅∇ u= up in RN, where p> 1 and a (x) is a
smooth vector field satisfying some decay conditions. We show that for p< pc, the Joseph …

We prove Liouville theorems for the double phase problem-div (|∇ u| p-2∇ u+ w (x)|∇ u| q-
2∇ u)= f (x)| u| r-1 u in RN, where q≥ p≥ 2, r> q-1 and w, f∈ L loc 1 (RN) are two …

Let and, we prove the nonexistence of positive stable solutions of weighted quasilinear
problem The result holds true for, or and, which is a positive critical exponent. Here and are …

We study the Kirchhoff equation of Hardy-Hénon type− a+ b∫ RN|∇ u| 2 dx Δ u=| x| p| u| q−
1 u in RN, where constants a, b≥ 0 and a+ b> 0. We show that this equation has no positive …

Positive entire solutions of the equation Δ _p u= u^-q in R^ N (N\geqslant 2) Δ pu= u− qin ℝ
N (N⩾ 2) where 1< p≤ N, q> 0, are classified via their Morse indices. It is seen that there is a …