Boundary blow-up elliptic problems with nonlinear gradient terms☆

By Zhijun Zhang. 2006

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By Karamata regular variation theory and perturbation method, we show the exact asymptotical behaviour of solutions near the boundary to nonlinear elliptic problems Δu±|∇u|q=b(x)g(u), u>0 in Ω, u|∂Ω=+∞, where Ω is a bounded domain with smooth boundary in RN, q⩾0, g∈C1[0,∞), g(0)=0, g′ is regularly varying at infinity with index ρ with ρ>0 and b is nonnegative nontrivial in Ω, which may be vanishing on the boundary.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/3a0a8536f9023439cfeaf96b498c3078e705611e