Research Communication | Open Access
Volume 2021 | Communication ID 312
Volume 2021 | Communication ID 312
| On the Lazer–McKenna conjecture for the fractional Laplacian |
Abdelrazek Dieb, Boumediene Abdellaoui, Fethi Mahmoudi
Received |
Accepted |
Published |
February 15, 2021 |
February 28, 2021 |
March 15, 2021 |
Abstract: We consider a class of Ambrosetti-Prodi problems with superlineair potential involving the fractional Laplacian and we prove the non-local version of a conjecture due to Lazer and McKenna which state that the solution set of the problem is unbounded for large parameter. Our argument relies on constructing solutions with sharp peaks near local maximum points of the first eigenfunction for the Fractional Laplacian with Dirichlet boundary data.