(untitled) (Journal of Partial Differential Equations, 2025)
In this work, we study the existence of one-sign solutions for the following problem: cases -Δ u = λ a(x) f(u), & in R^N, u(x) → 0, & as |x| → +∞. cases where N≥3, λ is a real parameter and a∈C_loc^α (R^N,R) for some α∈(0,1) is a weighted function, f: R→R is a Hölder continuous function with exponent α such that f(s)s>0 for any s e0. We determine the intervals of λ for the existence, exact multiplicity of one-sign solutions for this problem. We use bifurcation techniques and the approximation of connected components to prove our main results.