On the location of the peaks of least-energy solutions to semilinear Dirichlet problems with critical growth.
On the multiplicity of critical points for parameterized functionals on reflexive Banach spaces
Some general multiplicity results for critical points of parameterized functionals on reflexive Banach spaces are established. In particular, one of them improves some aspects of a recent result by B. Ricceri. Applications to boundary value problems are also given.
On the necessity of gaps
Recent papers have studied the existence of phase transition solutions for Allen–Cahn type equations. These solutions are either single or multi-transition spatial heteroclinics or homoclinics between simpler equilibrium states. A sufficient condition for the construction of the multitransition solutions is that there are gaps in the ordered set of single transition solutions. In this paper we explore the necessity of these gap conditions.
On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity
We consider the Neumann problem for the equation , u ∈ H¹(Ω), where Q is a positive and continuous coefficient on Ω̅ and λ is a parameter between two consecutive eigenvalues and . Applying a min-max principle based on topological linking we prove the existence of a solution.
On the nonlinear Neumann problem with critical and supercritical nonlinearities [Book]
On the number of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds.
On the rectifiability of domains with finite perimeter
On the regularity of a free boundary for a nonlinear obstacle problem arising in superconductor modelling
On the Schwarz algorithms for the elliptic exterior boundary value problems
Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...
On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems
Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...
On the second eigenvalue of a Hardy-Sobolev operator.
On the solvability of degenerated quasilinear elliptic problems.
On the solvability of semilinear elliptic equation via an associated eigenvaule problem.
On the solvability of superlinear and nonhomogeneous quasilinear equations.
On the stability of the free boundary in the obstacle problem for a minimal surface
On the two-phase membrane problem with coefficients below the Lipschitz threshold
On two problems studied by A. Ambrosetti
We study the Ambrosetti–Prodi and Ambrosetti–Rabinowitz problems.We prove for the first one the existence of a continuum of solutions with shape of a reflected (-shape). Next, we show that there is a relationship between these two problems.
On Two-Dimensional Quasi-Linear Elliptic Systems.
On Uniqueness of Boundary Values of Solutions of a Problem Arising in Plasma Physics.
On variations of the shape Hessian and sufficient conditions for the stability of critical shapes.
Para el estudio de la naturaleza de formas críticas en optimización de formas se requieren algunas propiedades de continuidad sobre las derivadas de segundo orden de las formas. Dado que la fórmula de Taylor-Young involucra a diferentes topologías que no son equivalentes, dicha fórmula no permite deducir cuando una forma crítica es un mínimo local estricto de la función forma pese a que su Hessiano sea definido positivo en ese punto. El resultado principal de este trabajo ofrece una cota superior...