Coercive estimates for a degenerate elliptic system of equations with spectral applications

In this work we derive a solvability result for a boundary value problem related to a degenerate elliptic system of second-order equations in the domain Ω = { ( x , y ) : − ∞ < y < ∞ , − π < x < π } . We analyze the problem of square integrability (with an appropriate weight) of the solution and its derivative, that arises in the case of degenerate systems with unbounded coefficients. In the second part of the study we establish some a priori and coercive estimates for the solution. The compactness of the resolvent and necessary estimates for the distribution function of s -numbers of the inverse operator L − 1 are obtained.