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We investigate second-term asymptotic behavior of boundary blow-up solutions to the problems Δu=b(x)f(u), x∈Ω, subject to the singular boundary condition u(x)=∞, in a bounded smooth domain Ω⊂RN. b(x) is a non-negative weight function. The nonlinearly f is regularly varying at infinity with index ρ>1 (that is limu→∞f(ξu)/f(u)=ξρ for every ξ>0) and the mapping f(u)/u is increasing on (0,+∞). The...
In this paper, combining the method of lower and upper solutions with the localization method, we establish the boundary blow-up rate of the large positive solutions to the singular boundary value problem {Δu=b(x)f(u),x∈Ω,u(x)=+∞,x∈∂Ω, where Ω is a smooth bounded domain in RN. The weight function b(x) is a non-negative continuous function in the domain, which vanishes on the boundary of the underlying...
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