Anello, GiovanniVilasi, Luca2022-03-102022-03-102018-11-20Anello, G., & Vilasi, L. (2018). Exactness of the number of positive solutions to a singular quasilinear problem. <i>Electronic Journal of Differential Equations, 2018</i>(189), pp. 1-12.1072-6691https://hdl.handle.net/10877/15485We study the exact multiplicity of positive solutions to the one-dimensional Dirichlet problem -(|u′|p-2 u′)′ = λu s-1 - μu r-1 in ]0, 1[ u(0) = u(1) = 0, where r ∈ ]0, 1[, p ∈ ]1, +∞[, r < s < p and λ, μ ∈ ]0, +∞[. We shed light, in particular, on the case r ∈ ]0, min{s, p/(p + 1)}[, completely determining the bifurcation diagram and solving some related open problems. Our approach relies upon quadrature methods.Text12 pages1 file (.pdf)enAttribution 4.0 Internationalexactnesssingular problemspositive solutionsquadrature methodArticle