On solvability for a class of quasilinear resonance elliptic equations

In this paper, we obtain an existence result for a class of high order quasilinear elliptic equations with higher eigenvalues. The proofs rely on Galerkin-type techniques, Brouwerʼs fixed points theorem. In this case, the nonlinearity is unbounded and satisfies sublinear growth. The equation is one of the most useful sets of Navier–Stokes equations, which describe the motion of viscous fluid substances such as liquids, gases and so on.