In this talk we discuss some recent results about a class of fully nonlinear second order partial differential problems in nondivergence form, uniformly elliptic with quadratic growth in the gradient. We show that multiplicity of solutions occurs up to the context of systems when the operator is not coercive, and we analyze the qualitative behavior of the continuums produced by a parameterized family of problems. Joint works with Boyan Sirakov and Delia Schiera.