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Solutions of nonlinear Schrödinger equation with fractional Laplacian without the Ambrosetti–Rabinowitz condition

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  • Gou, Tian-Xiang
  • Sun, Hong-Rui

Abstract

This paper is concerned with the existence of two nonnegative radial solutions of following nonlinear Schrödinger equation with fractional Laplacian(-Δ)αu+u=f(u)inRN,u∈Hα(RN),where 0<α<1. Under certain assumptions, we obtain that the above problem has at least two nontrivial radial solutions without assuming the Ambrosetti–Rabinowitz condition by variational methods and concentration compactness principle. The result extends one of the main results of Felmer et al. (2012).

Suggested Citation

  • Gou, Tian-Xiang & Sun, Hong-Rui, 2015. "Solutions of nonlinear Schrödinger equation with fractional Laplacian without the Ambrosetti–Rabinowitz condition," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 409-416.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:409-416
    DOI: 10.1016/j.amc.2014.09.035
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    Cited by:

    1. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.
    2. Mohammed Massar & Mohamed Talbi, 2021. "Radial solutions for a fractional Kirchhoff type equation in $$\mathbb {R}^N$$ R N," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(3), pages 897-902, September.

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