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<p>We consider the Lane–Emden equation with a supercritical nonlinearity with an inhomogeneous Dirichlet boundary condition on an infinite cone. Under suitable conditions for the boundary data and the exponent of nonlinearity, we give a complete classification of the existence/nonexistence of a solution with respect to the size of boundary data. Moreover, we give a result on the multiple existence of solutions via bifurcation theory. We also state results on Hardy–Hénon equations on infinite cones as a generalization.</p>

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Supercritical Lane–Emden equation on a cone with an inhomogeneous Dirichlet boundary condition

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  • 发表日期：

    2025年8月25日

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  • Sho Katayama

摘要

We consider the Lane–Emden equation with a supercritical nonlinearity with an inhomogeneous Dirichlet boundary condition on an infinite cone. Under suitable conditions for the boundary data and the exponent of nonlinearity, we give a complete classification of the existence/nonexistence of a solution with respect to the size of boundary data. Moreover, we give a result on the multiple existence of solutions via bifurcation theory. We also state results on Hardy–Hénon equations on infinite cones as a generalization.