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Sharp estimates for the Green function, 3G inequalities, and nonlinear Schrödinger problems in uniform cones

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Abstract

We find and prove sharp estimates for the Green function and 3G inequalities in uniform cones. These estimates are applied to give equivalent conditions for measures to satisfy the generalized Cranston-McConnell inequality, and to show the existence of infinitely many continuous positive solutions to certain nonlinear Schrödinger problems.

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Authors and Affiliations

  1. Department of Mathematics, Hokkaido University, 060-0810, Sapporo, Japan

    Kentaro Hirata

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  1. Kentaro Hirata
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Hirata, K. Sharp estimates for the Green function, 3G inequalities, and nonlinear Schrödinger problems in uniform cones. J. Anal. Math. 99, 309–332 (2006). https://doi.org/10.1007/BF02789450

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  • DOI: https://doi.org/10.1007/BF02789450

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