Abstract
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.
Citation
Satoshi Hashimoto. Mitsuharu Ôtani. "Elliptic equations with singularity on the boundary." Differential Integral Equations 12 (3) 339 - 349, 1999. https://doi.org/10.57262/die/1367265215
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