{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Z5TNUARUI3DOJUN4JT2PM5BMWE","short_pith_number":"pith:Z5TNUARU","schema_version":"1.0","canonical_sha256":"cf66da023446c6e4d1bc4cf4f6742cb1114cfce47bcfaf031874100c28adc162","source":{"kind":"arxiv","id":"1401.4400","version":3},"attestation_state":"computed","paper":{"title":"Remarks on two fourth order elliptic problems in whole space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baishun Lai, Dong Ye","submitted_at":"2014-01-17T16:23:36Z","abstract_excerpt":"We are interested in entire solutions for the semilinear biharmonic equation $\\Delta^{2}u=f(u)$ in $\\R^N$, where $f(u)=e^{u}$ or $-u^{-p}\\ (p>0)$. For the exponential case, we prove that any classical entire solution verifies $-\\Delta u>0$ without any restriction, which completes the results in \\cite{Dupaigne, xu-wei} and yields a nonexistence result in $\\R^2$ ; we obtain also a refined asymptotic expansion of radial separatrix solution for $N=3$, which answers a question in \\cite{Berchio}. For the negative power case, we show the nonexistence of the classical entire solution for any $00)$. For the exponential case, we prove that any classical entire solution verifies $-\\Delta u>0$ without any restriction, which completes the results in \\cite{Dupaigne, xu-wei} and yields a nonexistence result in $\\R^2$ ; we obtain also a refined asymptotic expansion of radial separatrix solution for $N=3$, which answers a question in \\cite{Berchio}. For the negative power case, we show the nonexistence of the classical entire solution for any $0