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.

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

FERRARA, Massimiliano
Supervision
;
2018

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12318/4593
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