The positive solutions to a quasi-linear problem of fractional p-Laplacian type without the Ambrosetti-Rabinowitz condition

Ferrara, Massimiliano; Bin, Ge; Ying-Xin, C.; Liang-Liang, S

doi:10.1007/s11117-018-0551-z

In this paper, we study the existence of nontrivial solution to a quasi-linear problem where is a nonlocal and nonlinear operator and , , , is a bounded domain which smooth boundary . Using the variational methods based on the critical points theory, together with truncation and comparison techniques, we show that there exists a critical value of the parameter, such that if , the problem has at least two positive solutions, if , the problem has at least one positive solution and it has no positive solution if . Finally, we show that for all , the problem has a smallest positive solution.

Titolo:	The positive solutions to a quasi-linear problem of fractional p-Laplacian type without the Ambrosetti-Rabinowitz condition
Autori:	FERRARA, Massimiliano [Supervision] Bin Ge [Methodology] (Corresponding) Ying-Xin C. [Methodology] Liang-Liang S [Writing – Review & Editing] mostra contributor esterni nascondi contributor esterni
Data di pubblicazione:	2018
Rivista:	POSITIVITY
Handle:	http://hdl.handle.net/20.500.12318/4593
Appare nelle tipologie:	1.1 Articolo in rivista

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