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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 4
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Articles

On a class of fractional Schrödinger equations in with sign-changing potential

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Pages 538-551 | Received 13 Aug 2016, Accepted 20 Dec 2016, Published online: 11 Jan 2017
 

Abstract

We are interested in finding solutions to a class of problems involving the fractional Laplacian operator. Specifically, we study the equation

where , denotes the fractional Laplacian of order s, , V(x) is a continuous and unbounded potential which may change sign, and the nonlinearity is a continuous function which may be unbounded in x since its growth is controlled by V(x) and has subcritical growth in in the sense of the Sobolev embedding. Assuming suitable conditions under V(x) and and applying a approach variational, we prove the existence of the multiplicity of solution for this equation.

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Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research partially supported by CNPq [grant number 308758/2013-7].

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