{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:QHBQO5B2YQTMCSTENJGOQGMTF6","short_pith_number":"pith:QHBQO5B2","schema_version":"1.0","canonical_sha256":"81c307743ac426c14a646a4ce819932f9361ae38fe7c4477744f2a2e2e522923","source":{"kind":"arxiv","id":"1010.2289","version":1},"attestation_state":"computed","paper":{"title":"On least Energy Solutions to A Semilinear Elliptic Equation in A Strip","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Henri Berestycki, Juncheng Wei","submitted_at":"2010-10-12T03:21:44Z","abstract_excerpt":"We consider the following semilinear elliptic equation on a strip: \\[ \\left\\{{array}{l} \\Delta u-u + u^p=0 \\ {in} \\ \\R^{N-1} \\times (0, L), u>0, \\frac{\\partial u}{\\partial \\nu}=0 \\ {on} \\ \\partial (\\R^{N-1} \\times (0, L)) {array} \\right.\\] where $ 1< p\\leq \\frac{N+2}{N-2}$. When $ 1

0$ such that for $L \\leq L_{*}$, the least energy solution is trivial, i.e., doesn't depend on $x_N$, and for $L >L_{*}$, the least energy solution is nontrivial. When $N \\geq 4, p=\\frac{N+2}{N-2}$, it is shown that there are two numbers $L_{*}0, \\frac{\\partial u}{\\partial \\nu}=0 \\ {on} \\ \\partial (\\R^{N-1} \\times (0, L)) {array} \\right.\\] where $ 1< p\\leq \\frac{N+2}{N-2}$. When $ 1

0$ such that for $L \\leq L_{*}$, the least energy solution is trivial, i.e., doesn't depend on $x_N$, and for $L >L_{*}$, the least energy solution is nontrivial. When $N \\geq 4, p=\\frac{N+2}{N-2}$, it is shown that there are two numbers $L_{*}