Bubbling solutions for an elliptic equation with exponential Neumann data in R<SUP>2</SUP>
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2014
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Abstract
Let Omega be a bounded domain in R-2 with smooth boundary; we study the following Neumann problem
{-Delta u + u = 0 in Omega
partial derivative u/partial derivative v = lambda u(p-1)e(up) on partial derivative Omega
where v is the outer normal vector of partial derivative Omega, lambda > 0 is a small parameter and 0 < p < 2. We construct bubbling solutions to problem (0.1) by a Lyapunov-Schmidt
{-Delta u + u = 0 in Omega
partial derivative u/partial derivative v = lambda u(p-1)e(up) on partial derivative Omega
where v is the outer normal vector of partial derivative Omega, lambda > 0 is a small parameter and 0 < p < 2. We construct bubbling solutions to problem (0.1) by a Lyapunov-Schmidt