Abstract
In this paper, we discuss several results regarding existence, multiplicity and stability of solutions of differential equation with discontinuous nonlinearities relevant in several applications. Our problem can be formulated as a free boundary problem with unknown boundaries to be characterized. We first show that the bifurcation diagram is a generalized ‘S-shaped’ curve. Then we study the stability of different parts of the bifurcation curve. Our approach is based on the comparison principle and some monotonicity arguments.
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