A Curve of Positive Solutions for an Indefinite Sublinear Dirichlet Problem - Ramos-Quoirin, H (American Institute of Mathematical Sciences, 2020)
We investigate the existence of a curve q 7→ uq, with q ∈ (0, 1), of positive solutions for the problem (− u ∆ = u 0 = a(x)uq in on Ω ∂ Ω, (Pa,q) where Ω is a bounded and smooth domain of RN and a : Ω → R is a sign-changing function (in which case the strong maximum principle does not hold). In addition, we analyze the asymptotic behavior of uq as q → 0+ and q → 1−. We also show that in some cases uq is the ground state solution of (Pa,q). As a byproduct, we obtain existence results for a singular and indefinite Dirichlet problem. Our results are mainly based on bifurcation and sub-supersolutions methods. © 2019 American Institute of Mathematical Sciences. All rights reserved.