Bibliographic Details
| Title: |
Uniqueness of Heteroclinic Solutions in a Class of Autonomous Quasilinear ODE Problems. |
| Authors: |
Alves, Claudianor O.1 (AUTHOR) coalves@mat.ufcg.edu.br, Isneri, Renan J. S.1 (AUTHOR) renanisneri@mat.ufcg.edu.br, Montecchiari, Piero2 (AUTHOR) p.montecchiari@staff.univpm.it |
| Source: |
Analysis & Applications. Oct2025, Vol. 23 Issue 7, p1093-1128. 36p. |
| Subject Terms: |
*Autonomous differential equations, *Uniqueness (Mathematics), *Laplacian operator, *Differential operators, *Differential equations, *Bifurcation theory |
| Abstract: |
In this paper, we prove the existence, uniqueness and qualitative properties of heteroclinic solution for a class of autonomous quasilinear ordinary differential equations of the Allen–Cahn type given by − ϕ (| u ′ |) u ′ ′ + V ′ (u) = 0 in ℝ , where V is a double-well potential with minima at t = ± α and ϕ : (0 , + ∞) → (0 , + ∞) is a C 1 function satisfying some technical assumptions. Our results include the classic case ϕ (t) = t p − 2 , which is related to the celebrated p -Laplacian operator, presenting the explicit solution in this specific scenario. Moreover, we also study the case ϕ (t) = 1 1 + t 2 , which is directly associated with the prescribed mean curvature operator. [ABSTRACT FROM AUTHOR] |
| Database: |
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