Mountain pass and linking type sign-changing solutions for nonlinear problems involving the fractional Laplacian

نویسندگان

  • Huxiao Luo
  • Xianhua Tang
  • Shengjun Li
چکیده

where ⊂Rn (n≥ 2) is a bounded smooth domain, s ∈ (0, 1), (– )s denotes the fractional Laplacian, λ is a real parameter, the nonlinear term f satisfies superlinear and subcritical growth conditions at zero and at infinity. When λ≤ 0, we prove the existence of a positive solution, a negative solution and a sign-changing solution by combing minimax method with invariant sets of descending flow. When λ≥ λ1 (where λ1 denotes the first eigenvalue of the operator (– ) s in with homogeneous Dirichlet boundary data), we prove the existence of a sign-changing solution by using a variation of linking type theorems.

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تاریخ انتشار 2017