Sublinear elliptic equations with singular coefficients on the boundary (Q632987)

The author studies a sublinear elliptic equation with singular coefficient on the boundary. The problem is considered in any bounded domain \(\Omega\) with zero Dirichlet boundary condition. It is proved that the equation has a unique positive solution and infinitely many sign-changing solutions which belong to \(C^1(\overline{\Omega})\) or \(C^2(\overline{\Omega})\). Moreover, it is proved that the solutions have higher order regularity corresponding to the smoothness of the coefficient.