A three solutions theorem for PUCCI’s extremal operator and its application

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A three solutions theorem for PUCCI’s extremal operator and its application

Year : 2021

Publisher : Juliusz Schauder Center for Nonlinear Analysis

Source Title : Topological Methods in Nonlinear Analysis

Document Type :

Abstract

In this article we prove a three solution type theorem for the following boundary value problem: (formula presented) where is a bounded smooth domain in RN and f: [0,∞] → [0,∞] is a Cα function. This is motivated by the work of Amann [3] and Shivaji [27], 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.