We prove the existence of a solution between an ordered pair of sub and supersolutions for singular quasilinear elliptic problems on unbounded domains. Further, we use this result to establish the existence of a positive solution to the problem {-Δpu=λK(x)f(u)in B1 c,u=0 on ∂B1, u(x)→0 as |x|→∞, where B1c={x ∈ ℝn||x|>1}, Δpu=div(|∇u|p-2∇u),1<p<n, λ is a positive parameter, K belongs to a class of functions which satisfy certain decay assumptions and f belongs to a class of (p-1)-subhomogeneous functions which may be singular at the origin, namely lim s→0+f(s)=-∞. Our methods can be also applied to establish a similar existence result when the domain is entire Rn. © 2014 Elsevier Ltd. All rights reserved.}, author_keywords={Infinite semipositone; p-Laplacian; Singular problems; Sub and supersolutions; Unbounded domains}, keywords={C (programming language), P-Laplacian; Semi-positone; Singular problem; Super-solutions; Unbounded domain, Computational mechanics}, funding_details={Grantová Agentura České RepublikyGrantová Agentura České Republiky, GA ČR, 13-00863S, EXLIZ - CZ.1.07/2.3.00/30.0013}, funding_details={European Social FundEuropean Social Fund, ESF}, funding_text_1={The first author was supported by the Grant Agency of Czech Republic, Project No. 13-00863S. The second author was funded by the project EXLIZ - CZ.1.07/2.3.00/30.0013, which is co-financed by the European Social Fund and the state budget of the Czech Republic.}, references={Lee, E.K., Shivaji, R., Ye, J., Classes of infinite semipositone systems (2009) Proc. Roy. Soc. Edinburgh Sect. 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Optim., 12 (3), pp. 191-202}, correspondence_address1={Drábek, P.; Department of Mathematics and NTIS, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, 301 00 Plzeň, Czech Republic; email: pdrabek@kma.zcu.cz}, publisher={Elsevier Ltd}, issn={0362546X}, coden={NOAND}, language={English}, abbrev_source_title={Nonlinear Anal Theory Methods Appl}, document_type={Article}, source={Scopus},