Complex Hessian equations extend the classical framework of the complex Monge–Ampère equation by involving the m-th elementary symmetric function of the eigenvalues of the complex Hessian. This ...

Assuming only asymptotic conditions on the potential function, we prove the existence of periodic solutions for equations whose nonlinearity stays below the first curve of Fučik's spectrum.

We prove that the Riemann zeta-function is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in Γ, Γ′ and Γ″ over the field of complex numbers.