{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VZBMRW7S3USMGCXBM46Y6TLHBZ","short_pith_number":"pith:VZBMRW7S","schema_version":"1.0","canonical_sha256":"ae42c8dbf2dd24c30ae1673d8f4d670e62b89ef40635be8a9556b366857383da","source":{"kind":"arxiv","id":"1711.01438","version":2},"attestation_state":"computed","paper":{"title":"Existence of heteroclinic solution for a double well potential equation in an infinite cylinder of $\\mathbb{R}^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves","submitted_at":"2017-11-04T13:48:59Z","abstract_excerpt":"This paper concernes with the existence of heteroclinic solutions for the following class of elliptic equations $$ -\\Delta{u}+A(\\epsilon x, y)V'(u)=0, \\quad \\mbox{in} \\quad \\Omega, $$ where $\\epsilon >0$, $\\Omega=\\R \\times \\D$ is an infinite cylinder of $\\mathbb{R}^N$ with $N \\geq 2$. Here, we have considered a large class of potential $V$ that includes the Ginzburg-Landau potential $V(t)=(t^{2}-1)^{2}$ and two geometric conditions on the function $A$. In the first condition we assume that $A$ is asymptotic at infinity to a periodic function, while in the second one $A$ satisfies $$ 00$, $\\Omega=\\R \\times \\D$ is an infinite cylinder of $\\mathbb{R}^N$ with $N \\geq 2$. Here, we have considered a large class of potential $V$ that includes the Ginzburg-Landau potential $V(t)=(t^{2}-1)^{2}$ and two geometric conditions on the function $A$. In the first condition we assume that $A$ is asymptotic at infinity to a periodic function, while in the second one $A$ satisfies $$ 0