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Logistic type equations on \(\mathbb R^N\) by a squeezing method involving boundary blow-up solutions. (English) Zbl 1018.35045

The authors study the diffusive logistic equation \[ u_t-\Delta u= \lambda u-u^p,\;u\geq 0, \;p>1, \tag{1} \] on the entire space and its generalization. Here they mainly interested in those properties of (1) which continue to hold when (1) is perturbed by the introduction of space variables, and the authors show that these properties resemble very much those of the bounded domain. To this end they use a squeezing method where boundary blow-up solutions are used as upper solutions.

MSC:

35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35J60 Nonlinear elliptic equations
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