Journal of the Mathematical Society of Japan

Sublinear elliptic equations with singular coefficients on the boundary

Ryuji KAJIKIYA

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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.

Article information

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

Dates
First available in Project Euclid: 27 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1296138352

Digital Object Identifier
doi:10.2969/jmsj/06310263

Mathematical Reviews number (MathSciNet)
MR2752440

Zentralblatt MATH identifier
1215.35054

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

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

Citation

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. https://projecteuclid.org/euclid.jmsj/1296138352


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