Boundary blow-up solutions for p-Laplacian elliptic equations of logistic type
2012 ◽
Vol 142
(4)
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pp. 691-714
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Keyword(s):
Blow Up
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We establish the existence, uniqueness and blow-up rate near the boundary of boundary blow-up solutions to p-Laplacian elliptic equations of logistic type −Δpu = a(x)h(u) − b(x)f(u), where Δpu = div (|∇u|p−2∇u) with p > 1, h(u)/up−1 is non-increasing and f(u) is a function whose variation at infinity may be regular or rapid. In particular, our result regarding the blow-up rate reveals the main difference between regular variation function f and rapid variation function f.