### Positive solutions for generalized nonlinear logistic equations of superdiffusive type

#### 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.

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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