Add to ORKGAbstract. Stability properties for solutions of −∆m(u) = f(u) in RN are investigated, where N ≥ 2 and m ≥ 2. The aim is to identify a critical dimension N # so that every non-constant solution is linearly unstable when-ever 2 ≤ N < N#. For positive, increasing and convex nonlinearities f(u), global bounds on f f (f ′)2 allows us to find a dimension N #, which is optimal for exponential and power nonlinearities. In the radial setting we can deal more generally with C1−nonlinearities and the dimension N # we find is still optimal
AbstractIn this note we give a complete answer to a question raised by Dupaigne and Farina (2009) [8...
AbstractThis paper is devoted to the study of semi-stable radial solutions u∈H1(B1) of −Δu=g(u) in B...
Let Ω := (a, b) ⊂ R, m ∈ L1 (Ω) and λ > 0 be a real parameter. Let L be the differential operator g...
(Communicated by Juncheng Wei) Abstract. Stability properties for solutions of −∆m(u) = f(u) in RN ...
Stability properties for solutions of $-\Delta_m(u)=f(u)$ in $\mathbb{R}^N$ are investigated, where ...
We study stable solutions to the equation (−∆)1/2u = f (u), posed in a bounded domain of Rn. For non...
Abstract. We consider the class of semi-stable positive solutions to semilinear equations −∆u = f(u)...
We establish that every nonconstant bounded radial solution u of −?u = f (u) in all of Rn is unstabl...
Several Liouville-type theorems are presented for stable solutions of the equation −∆u = f(u) in RN,...
Abstract: We study the stability of the branch of minimal solutions (u¸)0<¸<¸ ¤ of ¡¢u = ¸ g(...
AbstractWe consider a special class of radial solutions of semilinear equations −Δu=g(u) in the unit...
It is known that when the set of Lagrange multipliers associated with a stationary point of a constr...
Abstract. We consider the class of semi-stable positive solutions to semilin-ear equations −∆u = f(u...
This article is a survey on boundedness results for stable solutions to semilinear elliptic problems...
We start studing semi-stable solutions for the equation u = f(u) in a smooth and bounded domain of...
AbstractIn this note we give a complete answer to a question raised by Dupaigne and Farina (2009) [8...
AbstractThis paper is devoted to the study of semi-stable radial solutions u∈H1(B1) of −Δu=g(u) in B...
Let Ω := (a, b) ⊂ R, m ∈ L1 (Ω) and λ > 0 be a real parameter. Let L be the differential operator g...
(Communicated by Juncheng Wei) Abstract. Stability properties for solutions of −∆m(u) = f(u) in RN ...
Stability properties for solutions of $-\Delta_m(u)=f(u)$ in $\mathbb{R}^N$ are investigated, where ...
We study stable solutions to the equation (−∆)1/2u = f (u), posed in a bounded domain of Rn. For non...
Abstract. We consider the class of semi-stable positive solutions to semilinear equations −∆u = f(u)...
We establish that every nonconstant bounded radial solution u of −?u = f (u) in all of Rn is unstabl...
Several Liouville-type theorems are presented for stable solutions of the equation −∆u = f(u) in RN,...
Abstract: We study the stability of the branch of minimal solutions (u¸)0<¸<¸ ¤ of ¡¢u = ¸ g(...
AbstractWe consider a special class of radial solutions of semilinear equations −Δu=g(u) in the unit...
It is known that when the set of Lagrange multipliers associated with a stationary point of a constr...
Abstract. We consider the class of semi-stable positive solutions to semilin-ear equations −∆u = f(u...
This article is a survey on boundedness results for stable solutions to semilinear elliptic problems...
We start studing semi-stable solutions for the equation u = f(u) in a smooth and bounded domain of...
AbstractIn this note we give a complete answer to a question raised by Dupaigne and Farina (2009) [8...
AbstractThis paper is devoted to the study of semi-stable radial solutions u∈H1(B1) of −Δu=g(u) in B...
Let Ω := (a, b) ⊂ R, m ∈ L1 (Ω) and λ > 0 be a real parameter. Let L be the differential operator g...