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A general existence principle for strong solutions to the dirichlet problem for the equation δ u + f(t, u) = 0
(Elsevier BV, 1997-05-01)
An existence principle is established for Delta u + f(t, u) = 0 on Omega, u = 0 on partial derivative Omega. Our theory relies on a fixed point result for weakly sequentially continuous and weakly compact maps.