Heteroclinic solutions for a class of boundary value problems associated with singular equations. (July 2019)

• Record Type: Journal Article
• Authors: Biagi, Stefano; Calamai, Alessandro; Papalini, Francesca
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 44
• Page End: 68
• Publication Date: 2019-07
• Subjects: primary 34B40 34C37 34L30; Boundary value problems on unbounded domains -- Heteroclinic solutions -- Nonlinear differential operators -- Phi-Laplacian operators -- Singular equations -- Nagumo–Wintner growth condition; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.01.030
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We obtain existence results for strongly nonlinear BVPs of type (P) ( Φ ( k ( t ) x ′ ( t ) ) ) ′ = f ( t, x ( t ), x ′ ( t ) ) a.e. on [ 0, ∞ ), x ( 0 ) = ν 1, x ( ∞ ) = ν 2 where Φ : R → R is a strictly increasing homeomorphism such that Φ ( 0 ) = 0 (the Φ -Laplacian operator ), k : [ 0, ∞ ) → R is a non-negative continuous function which may vanish on a subset of [ 0, ∞ ) of measure zero, f is a Carathéodory function and ν 1, ν 2 ∈ R are fixed. Under mild assumptions, including a weak form of a Nagumo–Wintner growth condition, we prove the existence of heteroclinic solutions of(P) in the Sobolev space W loc 1, p ( [ 0, ∞ ) ) . Our approach is based on fixed point techniques suitably combined to the method of upper and lower solutions.