Exactness of the number of positive solutions to a singular quasilinear problem
Date
2018-11-20
Authors
Anello, Giovanni
Vilasi, Luca
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
exactness, singular problems, positive solutions, quadrature method
Citation
Anello, 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.
Rights
Attribution 4.0 International