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: | ||
Data di pubblicazione: | 2018 | |
Rivista: | ||
Handle: | http://hdl.handle.net/20.500.12318/4593 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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