2017/11/04 by Claudianor O. Alves, Alves, Claudianor O.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1711.01438
openalex publication_date 2017/11/04 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
This paper concernes with the existence of heteroclinic solutions for the\nfollowing class of elliptic equations -
Deltau+A(
epsilon x, y)V'(u)=0,\n
quad
mboxin
quad
Omega, where \ε >0, \Ω= R \× D is\nan infinite cylinder of \ℝN with N \≥ 2. Here, we have\nconsidered a large class of potential V that includes the Ginzburg-Landau\npotential V(t)=(t2-1)2 and two geometric conditions on the function\nA. In the first condition we assume that A is asymptotic at infinity to a\nperiodic function, while in the second one A satisfies \n0lt;A0=A(0,y)=
inf(x,y)
in
OmegaA(x,y) lt;
liminf|(x,y)|
to\n+
inftyA(x,y)=A_
inftylt;
infty,
quad
forall y
in
D.\n