Sublinear elliptic equations with singular coefficients on the boundary

Abstract

A sublinear elliptic equation whose coefficient is singular on the boundary is studied in any bounded domain Ω under the zero Dirichlet boundary condition. It is proved that the equation has a unique positive solution and infinitely many sign-changing solutions which belong to C¹($\overline{\Omega}$) or C²($\overline{\Omega}$). Moreover, it is proved that the solutions have the higher order regularity corresponding to the smoothness of the coefficient.