Abstract
We consider a generalized version of the $p$-logistic equation. Using variational methods based on the critical point theory and truncation techniques, we prove a bifurcation-type theorem for the equation. So, we show that there is a critical value $\lambda_*> 0$ of the parameter $\lambda> 0$ such that the following holds: if $\lambda> \lambda_*$, then the problem has two positive solutions; if $\lambda=\lambda_*$, then there is a positive solution; and finally, if $0< \lambda< \lambda_*$, then there are no positive solutions.
Citation
Antonio Iannizzotto. Nikolaos S. Papageorgiou. "Positive solutions for generalized nonlinear logistic equations of superdiffusive type." Topol. Methods Nonlinear Anal. 38 (1) 95 - 113, 2011.
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