Bound state for fractional Schrödinger equation with saturable nonlinearity

Youyan Wan and Zhengping Wang

Applied Mathematics and Computation, 2016, vol. 273, issue C, 735-740

Abstract: In this paper, we study the existence of bound state for the following fractional Schrödinger equation (P)(−Δ)αu+V(x)u=f(u),x∈RN,N≥3,where (−Δ)α with α ∈ (0, 1) is the fractional Laplace operator defined as a pseudo-differential operator with the symbol |ξ|2α, V(x) is a positive potential function and the nonlinearity f is saturable, that is, f(u)/u→l∈(0,+∞) as |u|→+∞. By using a variant version of Mountain Pass Theorem, we prove that there exists a bound state and ground state of (P) when V and f satisfy suitable assumptions.

Keywords: Fractional Schrödinger equation; Bound state; Ground state; Mountain Pass Theorem (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:273:y:2016:i:c:p:735-740

DOI: 10.1016/j.amc.2015.10.042

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