Patricio Felmer

Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian

We study the existence of positive solutions for the nonlinear Schrodinger equation with the fractional Laplacian Furthermore, we analyse the regularity, decay and symmetry properties of these solutions.

Multi-peak bound states for nonlinear Schrödinger equations

Abstract In this paper we consider the study of standing wave solutions for a nonlinear Schrodinger equation. This problem reduces to that of finding nonnegative solutions of ϵ 2 δu − V(x)u+ƒ(u)− in ω with finite energy. Here ϵ is a small parameter, ω is a smooth, possibly unbounded domain, f is an appropriate superlinear function, and V is a positive potential, bounded away from zero. It is the purpose of this article to obtain multi-peak solutions in the “multiple well case”. We find solutions exhibiting concentration at any prescribed finite set of local minima, possibly degenerate, of the potential. The proof relies on variational arguments, where a penalization-type method is developed for the identification of the desired solutions.

ON THE ROLE OF MEAN CURVATURE IN SOME SINGULARLY PERTURBED NEUMANN PROBLEMS

We construct solutions exhibiting a single spike-layer shape around some point of the boundary as

On the role of distance function in some singular perturbation problems

\var \to 0

Fundamental solutions and two properties of elliptic maximal and minimal operators

for the problem \left\{ \begin{array}{l} \var^2 \tri u - u + u^p = 0 \quad \mbox{in} \ \Omega, \\ u > 0 \quad \mbox{in} \ \Omega, \\ \frac{\partial u}{\partial \nu} = 0 \quad \mbox{on} \ \partial \Omega, \end{array} \right.\label {1.1} where

Least energy solutions for elliptic equations in unbounded domains

\Omega

Boundary blow up solutions for fractional elliptic equations

is a bounded domain with smooth boundary in

Local minimizers for the Ginzburg-Landau energy

R^N

Superlinear elliptic equation for fully nonlinear operators without growth restrictions for the data

,

Eigenvalues for Radially Symmetric Fully Nonlinear Operators

p > 1