Existence and nonexistence of blow-up boundary solutions for sublinear elliptic equations |
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Authors: | Haitao Yang |
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Institution: | Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China |
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Abstract: | In this paper we consider the semilinear elliptic problem Δu=a(x)f(u), u?0 in Ω, with the boundary blow-up condition u|∂Ω=+∞, where Ω is a bounded domain in RN(N?2), a(x)∈C(Ω) may blow up on ∂Ω and f is assumed to satisfy (f1) and (f2) below which include the sublinear case f(u)=um, m∈(0,1). For the radial case that Ω=B (the unit ball) and a(x) is radial, we show that a solution exists if and only if . For Ω a general domain, we obtain an optimal nonexistence result. The existence for nonradial solutions is also studied by using sub-supersolution method. |
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Keywords: | Sublinear elliptic equation Blow-up Sub-supersolution |
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