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Existence of entire explosive positive radial solutions of sublinear elliptic systems. (English) Zbl 1005.35038

Summary: Our main purpose is to establish the existence of entire explosive positive radial solutions of the quasilinear elliptic system \[ \text{div} \bigl(|\nabla u|^{p-2}\nabla u\bigr)= m \bigl(|x|\bigr)v^\alpha,\;x\in\mathbb R^N \]
\[ \text{div}\bigl( |\nabla v|^{q-2}\nabla v\bigr)= n\bigl(|x|\bigr) u^\beta,\;x\in \mathbb R^N \] where \(0<\alpha\leq p-1\), \(0<\beta\leq q-1\). The main results of the present paper are new and extend the previously known results [see, for example, A. V. Lair and A. W. Wood, J. Differ. Equations 164, No. 2, 380–394 (2000; Zbl 0962.35052)].

MSC:

35J45 Systems of elliptic equations, general (MSC2000)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)

Citations:

Zbl 0962.35052
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References:

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