Positivity preserving property for a class of biharmonic elliptic problems

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On a Fourth Order Elliptic Problem with a Singular Nonlinearity (2009, background): “These key-ingredients are missing in general when Dirichlet boundary conditions are considered (see [25, 3]) and just recently some symmetry results are obtained in [4].”
EXISTENCE OF NONTRIVIAL SOLUTIONS TO POLYHARMONIC EQUATIONS WITH SUBCRITICAL AND CRITICAL EXPONENTIAL GROWTH (2012, background): “It is worthwhile to notice that polyharmonic operators (−4) with Dirichlet boundary conditions in general do not satisfy the maximum principle if m ≥ 2 (see [5] for existence of minimal solutions for biLaplacian).”
On Positivity for the Biharmonic Operator under Steklov Boundary Conditions (2008, unknown): “The Steklov boundary conditions in (1) satisfy the complementing conditions, see [4].”
The First Biharmonic Steklov Eigenvalue: Positivity Preserving and Shape Optimization (2011, unknown): “From [3] we know that d1(B) = n, where B is the unit ball in R.”
On the first eigenvalue of a fourth order Steklov problem (2009, unknown): “Theorem 1 is already known in the case ∂Ω ∈ C2, see [4, 8, 9].”
On a fourth order Steklov eigenvalue problem (2005, background): “Let φ1 be a positive eigenfunction corresponding to the first eigenvalue d1 (see Theorem 1 in [4]).”