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Ground states for fractional Schrödinger equations involving a critical nonlinearity

Advances in Nonlinear Analysis, ISSN: 2191-950X, Vol: 5, Issue: 3, Page: 293-314
2016
  • 49
    Citations
  • 0
    Usage
  • 3
    Captures
  • 0
    Mentions
  • 17
    Social Media
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  • Citations
    49
    • Citation Indexes
      49
  • Captures
    3
  • Social Media
    17
    • Shares, Likes & Comments
      17
      • Facebook
        17

Article Description

This paper is aimed to study ground states for a class of fractional Schrödinger equations involving the critical exponents: (-Δ) u + u = λf(u) + |u|u in ℝ, where λ is a real parameter, (-Δ) is the fractional Laplacian operator with 0 < α < 1, 2 = 2N/N - 2α with 2 ≤ N, f is a continuous subcritical nonlinearity without the Ambrosetti-Rabinowitz condition. Based on the principle of concentration compactness in the fractional Sobolev space and radially decreasing rearrangements, we obtain a nonnegative radially symmetric minimizer for a constrained minimization problem which has the least energy among all possible solutions for the above equations, i.e., a ground state solution.

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