Remarks on large solutions of a class of semilinear elliptic equations
نویسندگان
چکیده
In this paper, we show existence, uniqueness and exact asymptotic behavior of solutions near the boundary to a class of semilinear elliptic equations −∆u = λg(u)− b(x)f(u) in Ω, where λ is a real number, b(x) > 0 in Ω and vanishes on ∂Ω. The special feature is to consider g(u) and f(u) to be regularly varying at infinity and b(x) is vanishing on the boundary with a more general rate function. The vanishing rate of b(x) determines the exact blow-up rate of the large solutions. And the exact blow-up rate allows us to obtain the uniqueness result.
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