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Title: Heteroclinic solutions for classical and singular φ-Laplacian non-autonomous differential equations
Authors: Minhós, Feliz
Keywords: ϕ-Laplacian operator
ean curvature operator
heteroclinic solutions
problems in the real line
Issue Date: 15-Feb-2019
Publisher: MDPI
Citation: Minhós, F. Heteroclinic Solutions for Classical and Singular ϕ-Laplacian Non-Autonomous Differential Equations. Axioms 2019, 8, 22.
Abstract: In this paper, we consider the second order discontinuous differential equation in the real line, (a(t,u)ϕ(u′))′=f(t,u,u′),a.e.t∈R,u(−∞)=ν−,u(+∞)=ν+, with ϕ an increasing homeomorphism such that ϕ(0)=0 and ϕ(R)=R, a∈C(R2,R) with a(t,x)>0 for (t,x)∈R2, f:R3→R a L1-Carathéodory function and ν−,ν+∈R such that ν−<ν+. 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 ϕ and f. To the best of our knowledge, this result is even new when ϕ(y)=y, that is for equation (a(t,u(t))u′(t))′=f(t,u(t),u′(t)),a.e.t∈R. Moreover, these results can be applied to classical and singular ϕ-Laplacian equations and to the mean curvature operator.
ISSN: EISSN 2075-1680
Type: article
Appears in Collections:MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica
CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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