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Characterization for the existence of bounded solutions to elliptic equations

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  • We give necessary and sufficient conditions for which the elliptic equation

    $\Delta u = \rho (x)\Phi (u)\;\;\;\;{\rm{in}}\;\;\;\;{\mathbb{R}^d}\;\;\;(d \ge 3)$

    has nontrivial bounded solutions.

    Mathematics Subject Classification: Primary: 31B05, 35B08; Secondary: 35J08, 35J91.


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