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Santos J\\'unior","submitted_at":"2013-04-16T19:19:57Z","abstract_excerpt":"Using minimax methods and Lusternik-Schnirelmann theory, we study multiple positive solutions for the Schr\\\"{o}dinger - Kirchhoff equation $$ M\\left(\\dis\\int_{\\Omega_{\\lambda}}|\\nabla u|^{2}dx+\\dis\\int_{\\Omega_{\\lambda}}u^{2}dx\\right)\\left[-\\Delta u + u \\right]= f(u) $$ in $\\Omega_{\\lambda} = \\lambda\\Omega$. The set $\\Omega \\subset \\mathbb{R}^3$ is a smooth bounded domain, $\\lambda>0$ is a parameter, $M$ is a general continuous function and $f$ is a superlinear continuous function with subcritical growth. 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