We consider the boundary value problem Δu+u^p=0 in a bounded, smooth domain Ω in R^2 with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Ω which ensure the existence of a positive solution up concentrating at exactly m points as p → ∞. In particular, for a non simply connected domain such a solution exists for any given m\geq 1.
Esposito, P., Musso, M., Pistoia, A. (2006). Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent. JOURNAL OF DIFFERENTIAL EQUATIONS, 227(1), 29-68 [10.1016/j.jde.2006.01.023].
Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent
ESPOSITO, PIERPAOLO;
2006-01-01
Abstract
We consider the boundary value problem Δu+u^p=0 in a bounded, smooth domain Ω in R^2 with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Ω which ensure the existence of a positive solution up concentrating at exactly m points as p → ∞. In particular, for a non simply connected domain such a solution exists for any given m\geq 1.File in questo prodotto:
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