On the existence of solutions to a fourth-order quasilinear resonant problem.
In this paper we deal with the stationary Navier-Stokes problem in a domain with compact Lipschitz boundary and datum in Lebesgue spaces. We prove existence of a solution for arbitrary values of the fluxes through the connected components of , with possible countable exceptional set, provided is the sum of the gradient of a harmonic function and a sufficiently small field, with zero total flux for bounded.
We propose a necessary and sufficient condition about the existence of variations, i.e., of non trivial solutions to the differential inclusion .
In this paper we prove the existence of a weak solution for a given semilinear singular real hyperbolic system.
Following the ideas of D. Serre and J. Shearer (1993), we prove in this paper the existence of a weak solution of the Cauchy problem for a given second order quasilinear hyperbolic equation.