Generalized limit theorem and bifurcation for problems with Pucci’s operator - Dai, Guowei (Topological Methods in Nonlinear Analysis, 2020)
We establish a new limiting result which extends the famous Whyburn’s limit theorem. As applications, we study the existence and multiplicity of one-sign or sign-changing solutions with a prescribed number of simple zeros for the following problem equation* cases -M_λ,Λ^+(D^2 u)=μ f(u) &in Ω, u=0&on Ω, cases equation* where M_λ,Λ^+ denotes the Pucci extremal operator. Combining bifurcation approach with our generalized limit theorem, we determine the range of parameter μ in which the above problem has one or multiple one-sign or sign-changing solutions according to the behaviors of f at 0 and ∞, and whether f satisfies the signum condition f(s)s> 0 for s eq0.