Heteroclinic Solutions for Classical and Singular ϕ-Laplacian Non-Autonomous Differential Equations
Departamento de Matemática, Escola de Ciências e Tecnologia, Centro de Investigação em Matemática e Aplicações (CIMA), Instituto de Investigação e Formação Avançada, Universidade de Évora. Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
Axioms 2019, 8(1), 22; https://doi.org/10.3390/axioms8010022
Received: 28 December 2018 / Revised: 28 January 2019 / Accepted: 11 February 2019 / Published: 15 February 2019
(This article belongs to the Special Issue New Trends in Differential and Difference Equations and Applications)
In this paper, we consider the second order discontinuous differential equation in the real line, with an increasing homeomorphism such that and , with for , a -Carathéodory function and such that . The existence and localization of heteroclinic connections is obtained assuming a Nagumo-type condition on the real line and without asymptotic conditions on the nonlinearities and . To the best of our knowledge, this result is even new when , that is for equation . Moreover, these results can be applied to classical and singular -Laplacian equations and to the mean curvature operator.
View Full-Text
Keywords:
ϕ-Laplacian operator; mean curvature operator; heteroclinic solutions; problems in the real line; lower and upper solutions; Nagumo condition on the real line; fixed point theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Minhós, F. Heteroclinic Solutions for Classical and Singular ϕ-Laplacian Non-Autonomous Differential Equations. Axioms 2019, 8, 22.
AMA Style
Minhós F. Heteroclinic Solutions for Classical and Singular ϕ-Laplacian Non-Autonomous Differential Equations. Axioms. 2019; 8(1):22.
Chicago/Turabian StyleMinhós, Feliz. 2019. "Heteroclinic Solutions for Classical and Singular ϕ-Laplacian Non-Autonomous Differential Equations" Axioms 8, no. 1: 22.
Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
Search more from Scilit