A Liouville-Type Theorem for the Lane–Emden Equation in a Half-space

Abstract We prove that the Dirichlet problem for Lane–Emden equation in a half-space has no positive solution is monotone normal direction. As consequence, this does not admit any classical bounded on finite strips. This question long history and our result solves long-standing open problem. Such nonexistence was previously available only solutions or under restriction power nonlinearity. The extends to general convex nonlinearities.