Differential and Integral Equations

Elliptic equations with singularity on the boundary

Satoshi Hashimoto and Mitsuharu Ôtani

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The existence and nonexistence of positive classical solutions is discussed for $-\Delta u = K(x) (1-|x|)^{- \alpha} u^{\beta}$ in the unit ball $B$ with Dirichlet boundary condition ${u |_{\partial B}= 0 }$. Our main tools are based on the variational method and Pohozaev's identity. The singularity of coefficients on the boundary will be handled with the symmetry of functions and some approximation procedures.

Article information

Differential Integral Equations, Volume 12, Number 3 (1999), 339-349.

First available in Project Euclid: 29 April 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations


Hashimoto, Satoshi; Ôtani, Mitsuharu. Elliptic equations with singularity on the boundary. Differential Integral Equations 12 (1999), no. 3, 339--349. https://projecteuclid.org/euclid.die/1367265215

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