Asymptotic behavior of large solutions to \(p\)-Laplacian of Bieberbach-Rademacher type. (English) Zbl 1176.35080
Summary: By the Karamata regular variation theory and the method of lower and upper solutions, we establish the asymptotic behavior of boundary blow-up solutions of the quasilinear elliptic equation \(\text{div}(|\nabla_u|^{p-2}\nabla u)=b(x)f(u)\) in a bounded \(\Omega \subset\mathbb R^N\) subject to the singular boundary condition \(u(x)=\infty \), where the weight \(b(x)\) is non-negative and non-trivial in \(\Omega \), which may be vanishing on the boundary or unbounded, the nonlinear term \(f\) is a \(\Gamma \)-varying function at infinity, whose variation at infinity is not regular.
MSC:
| 35J62 | Quasilinear elliptic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B44 | Blow-up in context of PDEs |
| 35J20 | Variational methods for second-order elliptic equations |
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