We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modelling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions...

Let Ω ⊂ ℝ be a smooth bounded domain. We give necessary and su cient conditions for the existence of positive solutions for sublinear Dirichlet periodic parabolic problems = (, , ) in Ω × ℝ for a wide class of Caratheodory functions : Ω × ℝ [0, ∞) → ℝ satisfying some...

Let Ω be a bounded domain in ℝ We characterize the set of positive principal eigenvalues for the Dirichlet periodic parabolic problem = λ () in Ω × ℝ, under the assumptions that is a function such that ζ → () is continuously differentiable and nonincreasing in [0, ∞) a.e. () ∈ Ω...