Abstract
We consider, respectively, the Dirichlet problem and the initial-boundary value problem of elliptic and parabolic equations with two power nonlinearities. We find that these problems are closely related to the so-called quenching problem. We obtain the existence and nonexistence of positive solutions to these problems on bounded and unbounded domains, by using the results of quenching problem and sub-super solution method.
Citation
Qiuyi Dai. Yonggeng Gu. "Positive solutions of elliptic and parabolic equations with convex-concave nonlinearities." Tohoku Math. J. (2) 57 (3) 427 - 445, September 2005. https://doi.org/10.2748/tmj/1128703005
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