Positive solutions and bifurcation phenomena for nonlinear elliptic equationsof logistic type: The superdiffusive case
Michael Ε. Filippakis, Donal O’Regan, Nikolaos S. Papageorgiou · Communications on Pure & Applied Analysis · 2010
We consider a nonlinear elliptic equation of logistictype, driven by the $p$-Laplacian differential operator with ageneral superdiffusive reaction. We show that the equationexhibits a bifurcation phenomenon. Namely there is a criticalvalue $\lambda_*$ of the parameter $\lambda>0$, such that, if$\lambda>\lambda_*$, the equation has two nontrivial positivesmooth solutions, if $\lambda=\lambda_*,$ then there is onepositive solution and finally if $\lambda\in (0,\lambda_*),$ thenthere is no positive solution.