Sublinear elliptic equations with singular coefficients on the boundary

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  • Kajikiya Ryuji
    Department of Mathematics, Faculty of Science and Engineering, Saga University

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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.

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