Marcelo Montenegro

Multidimensional boundary layers for a singularly perturbed Neumann problem

School of Mathematics Institute for Advanced Study 1 Einstein Drive Princeton, New Jersey 08540 USA Universidade Estadual de Campinas, IMECC, Departamento de Matematica, Caixa Postal 6065, CEP 13083-859, Campinas, SP, Brasil abstract. We continue the study of [34], proving concentration phenomena for the equation−e∆u+u = u in a smooth bounded domain Ω ⊆ R and with Neumann boundary conditions. The exponent p is greater or equal than 1 and the parameter e is converging to zero. For a suitable sequence ej → 0 we prove existence of positive solutions uj concentrating at the whole boundary of Ω or at some of its components.

STABLE SOLUTIONS FOR THE BILAPLACIAN WITH EXPONENTIAL NONLINEARITY.

Let

Positive versus free boundary solutions to a singular elliptic equation

\lambda^*>0

Existence and asymptotic behavior for a singular parabolic equation

denote the largest possible value of

MINIMAL SOLUTIONS FOR A CLASS OF ELLIPTIC SYSTEMS

\lambda

The sub-supersolution method for weak solutions

such that {

An Ambrosetti–Prodi-type result for a quasilinear Neumann problem

\Delta^2 u = \la e^u \ \text{in B, } u = \pd{u}{n} = 0 \ \text{on

Positive solutions for nonlinear elliptic equations with fast increasing weights

B

Existence of a positive solution for a singular system

}\}

Solutions to the nonlinear Schrödinger equation carrying momentum along a curve

has a solution, where B is the unit ball in