A three solutions theorem for Pucci’s extremal operator and its application - Mallick, Mohan; Verma, Ram Baran (Topological Methods in Nonlinear Analysis, 2021)
In this article we prove a three solution type theorem for the following boundary value problem: equation* abs cases -M_λ,Λ^+(D^2u) =f(u)& in Ω, u =0& on Ω, cases equation* where Ω is a bounded smooth domain in R^N and f[0,∞]→[0,∞] is a C^α function. This is motivated by the work of Amann aman and Shivaji shivaji1987remark, where a three solutions theorem has been established for the Laplace operator. Furthermore, using this result we show the existence of three positive solutions to above boundary value by explicitly constructing two ordered pairs of sub and supersolutions when f has a sublinear growth and f(0)=0.