Existence and concentration of solutions to elliptic systems with Neumann boundary conditions.

Author(s)

Marcos Tadeu de Oliveira Pimenta

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2008-03-13

Examining board members

Sérgio Henrique Monari Soares; Claudianor Oliveira Alves; Eugenio Tommaso Massa

• Advisor: Sérgio Henrique Monari Soares

Abstract

We study an singularly perturbed Hamiltonean elliptic system - \'elipson POT 2\' \'DELTA\' u + u = g(v) in \'ÔMEGA\' - \'elipson POT 2\' \'DELTA\' v + v f(u) in ÔMEGA \' PARTIAL\'u ON \'PARTIAL n = \'PARTIAL v ON PARTIAL n\' = O sobre \"PARTIAL\'\' ÔMEGA\' when \'ÔMEGA THIS CONTAINED R POT. N\' is a smooth bounded domain, N \' > or =\' 3 and f and g are nonlinearities having superlinear and subcritical growth at infinity. We study an abstract result about existence of critical points of strongly as \' epsilon\' goes to zero, at a point of the boundary which maximizes the mean curvature of the boundary (AU)

• FAPESP's process: 05/02717-3 - Existence and concentration of solutions to elliptic systems with Neumann boundary conditions
• Grantee: Marcos Tadeu de Oliveira Pimenta
• Support Opportunities: Scholarships in Brazil - Master