Remarks on large solutions of a class of semilinear elliptic equations |
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Authors: | Peng Feng |
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Institution: | Department of Chemistry and Mathematics, Florida Gulf Coast University, 10501 FGCU Blvd, S., Fort Myers, FL 33965, USA |
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Abstract: | In this paper, we show existence, uniqueness and exact asymptotic behavior of solutions near the boundary to a class of semilinear elliptic equations −Δu=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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Keywords: | Large solution Elliptic equation Regular variation |
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