Related papers: Compactness results and applications to some "zero…
This paper deals with the lack of compactness in nonlinear elliptic problems $(P)$. In particular, a domain $\Omega$ is provided where not converging Palais-Smale sequences exist at every energy level. Nevertheless, it is proved that…
We provide new results on the existence of nonzero positive weak solutions for a class of second order elliptic systems. Our approach relies on a combined use of iterative techniques and classical fixed point index. Some examples are…
This paper is devoted to the study, with variational technique, of (p,q)-Laplacian equations in presence of general nonlinearities. Especially we obtain the existence result for the zero mass case, which includes a large class of pure power…
We prove a global compactness result for Palais-Smale sequences associated with a class of quasi-linear elliptic equations on exterior domains.
We present an approach to minimization under constraint. We explore the connections of this technique with the general method of Compactness by Concentration of P.L. Lions and present applications to some constrained semi-linear and…
We obtain symmetry results for solutions of an elliptic system of equation possessing a cooperative structure. The domain in which the problem is set may possess "holes" or "small vacancies" (measured in terms of capacity) along which the…
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition…
We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are…
We discuss variational problems on two-dimensional domains with energy densities of linear growth and with radially symmetric data. The smoothness of generalized minimizers is established under rather weak ellipticity assumptions. Further…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
We are interested in the global solutions to a class of Klein-Gordon equations, and particularly in the unified time decay results with respect to the possibly vanishing mass parameter. We give for the first time a rigorous proof, which…
In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which…
In this manuscript we review some recent results about approximation of solutions of elliptic problems with high-contrast coefficients. In particular, we detail the derivation of asymptotic expansions for the solution in terms of the…
Given $N\geq 3$, $1<p<N$, two measurable functions $V\left(r \right)\geq 0$, $K\left(r\right)> 0$ and a continuous function $A(r) >0$ ($r>0$), we study the quasilinear elliptic equation \[ -\mathrm{div}\left(A(|x| )|\nabla u|^{p-2} \nabla…
We give blow-up behavior for solutions to an elliptic system with Dirichlet condition, and, weight and boundary singularity. Also, we have a compactness result for this elliptic system with regular H{\"o}lderian weight and boundary…
We look for positive solutions to the nonlinear Schrodinger equation with a potential, under the hypothesis of zero mass on the nonlinearity, in a particular situation. Existence and multiplicity results are provided.
In this paper we prove symmetry results for classical solutions of semilinear cooperative elliptic systems in R^N, or in the exterior of a ball. We consider the case of fully coupled systems and nonlinearities which are either convex or…
We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…