Positive solutions for generalized nonlinear logistic equations of superdiffusive type
Keywords
Generalized p-logistic equation, superdiffusive case, p-Laplacian, nonlinear maximum principle, positive solution, comparison theoremAbstract
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.Downloads
Published
2011-04-23
How to Cite
1.
IANNIZZOTTO, Antonio and PAPAGEORGIOU, Nikolaos S. Positive solutions for generalized nonlinear logistic equations of superdiffusive type. Topological Methods in Nonlinear Analysis. Online. 23 April 2011. Vol. 38, no. 1, pp. 95 - 113. [Accessed 26 April 2024].
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