Positive solutions of a degenerate elliptic equation with logistic reaction

Takeuchi, Shingo

doi:10.1090/S0002-9939-00-05723-3

Positive solutions of a degenerate elliptic equation with logistic reaction
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Proc. Amer. Math. Soc. 129 (2001), 433-441 Request permission

Abstract:

The degenerate elliptic equation $\lambda \Delta _p u +u^{q-1}(1-u^r)=0$ with zero Dirichlet boundary condition, where $\lambda$ is a positive parameter, $2<p<q$ and $r>0$, is studied in three aspects: existence of maximal solution, $\lambda$-dependence of maximal solution and multiplicity of solutions.

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