Boundary blow-up elliptic problems of Bieberbach and Rademacher type with nonlinear gradient terms. (English) Zbl 1131.35026
Summary: By a perturbation method and constructing comparison functions, we show the exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems \(\Delta u\pm|\nabla u|^q= b(x)e^u\), \(x\in\Omega\), \(u|_{\partial\Omega} =+\infty\), where \(\Omega\) is a bounded domain with smooth boundary in \(\mathbb R^N\), \(q\geq0\), \(b\) is non-negative and non-trivial in \(\Omega\), which may be vanishing on the boundary.
Keywords:
semilinear elliptic equations; nonlinear gradient terms; large solutions; asymptotic behaviourReferences:
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