Solutions of the fractional Schrodinger equation with a sign-changing nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:450

Article

Bieganowski, Bartosz¹ 

[1] Nicholas Copernicus Univ, Fac Math & Comp Sci, Ul Chopina 12-18, PL-87100 Torun, Poland

关键词: Variational methods;    Nehari manifold;    Fractional Schrodinger equation;    Periodic and localized potentials;    Coercive potential;    Sign-changing nonlinearity;   

DOI  :  10.1016/j.jmaa.2017.01.037

来源: Elsevier

【 摘 要 】

We look for solutions to a nonlinear, fractional Schrodinger equation (-Delta)(alpha/2)u + V(x)u = f(x, u) - Gamma(x)vertical bar u vertical bar(q-2)u on R-N, where the potential V is coercive or V = V-per + V-loc is a sum of a periodic in x potential V-per and a localized potential V-loe, Gamma is an element of L-infinity (R-N) is periodic in x, Gamma(x) >= 0 for a.e. x is an element of R-N and 2 < q < 2(alpha)*. If f has the subcritical growth, but higher than Gamma(x)vertical bar u vertical bar(q-2), then we find a ground state solution being a rninimiver on the Nehari manifold. Moreover we show that if f is odd in n and V is periodic, this equation admits infinitely many solutions, which are pairwise geometrically distinct. Finally, we obtain the existence result in the case of coercive potential V. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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