Journal of the Mathematical Society of Japan

Sublinear elliptic equations with singular coefficients on the boundary


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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.

Article information

J. Math. Soc. Japan, Volume 63, Number 1 (2011), 263-294.

First available in Project Euclid: 27 January 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 35J25: Boundary value problems for second-order elliptic equations 35J75: Singular elliptic equations

sublinear elliptic equation singular coefficient positive solution infinitely many solutions variational method


KAJIKIYA, Ryuji. Sublinear elliptic equations with singular coefficients on the boundary. J. Math. Soc. Japan 63 (2011), no. 1, 263--294. doi:10.2969/jmsj/06310263.

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