# Positive Solutions for the Neumann p-Laplacian with Superdiffusive Reaction

Bulletin of the Malaysian Mathematical Sciences Society, Aug 2015

We consider a generalized logistic equation driven by the Neumann p-Laplacian and with a reaction that exhibits a superdiffusive kind of behavior. Using variational methods based on the critical point theory, together with truncation and comparison techniques, we show that there exists a critical value $\lambda _*>0$ of the parameter, such that if $\lambda >\lambda _*$, the problem has at least two positive solutions, if $\lambda =\lambda _*$, the problem has at least one positive solution and it has no positive solution if $\lambda \in (0,\lambda _*)$. Finally, we show that for all $\lambda \geqslant \lambda _*$, the problem has a smallest positive solution.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2Fs40840-015-0212-3.pdf

Leszek Gasiński, Nikolaos S. Papageorgiou. Positive Solutions for the Neumann p-Laplacian with Superdiffusive Reaction, Bulletin of the Malaysian Mathematical Sciences Society, 2017, 1711-1731, DOI: 10.1007/s40840-015-0212-3