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Liouville-Type Theorem for Finite Morse Index Weak Solutions of Fourth-Order Nonlinear Equations

Shiyu Xia

Abstract


This paper studies the finite Morse index weak solutions of the fourth-order nonlinear Hénon-Lane-Emden equation ∆²u=|x|∂|u|p-1u in  RN  , where −4<α<0, 1<p<(N+4+2α)/(N−4) , and N≥5, proving a Liouville-type theorem. By selecting appropriate truncation functions and using Young’s inequality, Hölder’s inequality, and the Pohozaev identity, the related results are obtained.

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References


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DOI: http://dx.doi.org/10.70711/frim.v2i9.5258

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