Positive solutions for generalized nonlinear logistic equations of superdiffusive type

Antonio Iannizzotto, Nikolaos S. Papageorgiou

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.

Keywords


Generalized p-logistic equation; superdiffusive case; p-Laplacian; nonlinear maximum principle; positive solution; comparison theorem

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