Add to ORKGAbstract: We study the stability of the branch of minimal solutions (u¸)0<¸<¸ ¤ of ¡¢u = ¸ g(u) for a nonlinearity g which is neither concave nor convex. We show that it is related to the regularity of the map ¸ 7! u¸. We then show that in dimensions N = 1 and N = 2, discontinuities in the branch of minimal solutions can be produced by arbitrarilly small perturbations of the nonlinearity g. In dimensions N ¸ 3 the perturbation has to be large enough. We also study in detail a speci¯c one-dimensional example.
We study stable solutions to the equation (−∆)1/2u = f (u), posed in a bounded domain of Rn. For non...
We use the degree introduced by P. Benevieri and M. Furi [3] to obtain the generalized minimal cardi...
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolutio...
(Communicated by Juncheng Wei) Abstract. Stability properties for solutions of −∆m(u) = f(u) in RN ...
Abstract. Stability properties for solutions of −∆m(u) = f(u) in RN are investigated, where N ≥ 2 a...
These notes record the lectures for the CIME Summer Course taught by the first author in Cetraro dur...
Stability properties for solutions of $-\Delta_m(u)=f(u)$ in $\mathbb{R}^N$ are investigated, where ...
We consider the following Dirichlet problem(formula persented) and f non-negative and non-decreasing...
It is known that when the set of Lagrange multipliers associated with a stationary point of a constr...
AbstractWe consider a special class of radial solutions of semilinear equations −Δu=g(u) in the unit...
There exists a set $\cal U$ in the plane, such that elements of $\cal U$ correspond to minimal stabl...
The Bernoulli problem has been well studied since Alt-Caffarelli's s paper in '81. It consists in a ...
AbstractWe consider the following nonlinear elliptic equation with singular nonlinearity:Δu−1uα+a1uβ...
We prove optimal convergence results for discrete approximations to (possibly unstable) minimal surf...
There exists a set U in the plane, such that elements of U correspond to minimal stable solutions of...
We study stable solutions to the equation (−∆)1/2u = f (u), posed in a bounded domain of Rn. For non...
We use the degree introduced by P. Benevieri and M. Furi [3] to obtain the generalized minimal cardi...
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolutio...
(Communicated by Juncheng Wei) Abstract. Stability properties for solutions of −∆m(u) = f(u) in RN ...
Abstract. Stability properties for solutions of −∆m(u) = f(u) in RN are investigated, where N ≥ 2 a...
These notes record the lectures for the CIME Summer Course taught by the first author in Cetraro dur...
Stability properties for solutions of $-\Delta_m(u)=f(u)$ in $\mathbb{R}^N$ are investigated, where ...
We consider the following Dirichlet problem(formula persented) and f non-negative and non-decreasing...
It is known that when the set of Lagrange multipliers associated with a stationary point of a constr...
AbstractWe consider a special class of radial solutions of semilinear equations −Δu=g(u) in the unit...
There exists a set $\cal U$ in the plane, such that elements of $\cal U$ correspond to minimal stabl...
The Bernoulli problem has been well studied since Alt-Caffarelli's s paper in '81. It consists in a ...
AbstractWe consider the following nonlinear elliptic equation with singular nonlinearity:Δu−1uα+a1uβ...
We prove optimal convergence results for discrete approximations to (possibly unstable) minimal surf...
There exists a set U in the plane, such that elements of U correspond to minimal stable solutions of...
We study stable solutions to the equation (−∆)1/2u = f (u), posed in a bounded domain of Rn. For non...
We use the degree introduced by P. Benevieri and M. Furi [3] to obtain the generalized minimal cardi...
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolutio...