Positive solutions for generalized nonlinear logistic equations of superdiffusive type
KeywordsGeneralized p-logistic equation, superdiffusive case, p-Laplacian, nonlinear maximum principle, positive solution, comparison theorem
AbstractWe 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.
How to Cite
IANNIZZOTTO, Antonio & PAPAGEORGIOU, Nikolaos S. Positive solutions for generalized nonlinear logistic equations of superdiffusive type. Topological Methods in Nonlinear Analysis [online]. 23 April 2011, T. 38, nr 1, s. 95–113. [accessed 8.12.2022].
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