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Multiplicity results for a nonlinear elliptic problem involving the fractional Laplacian. (English) Zbl 1374.35164

Summary: In this paper, we consider a class of superlinear elliptic problems involving fractional Laplacian \((-\Delta)^{s/2}u = \lambda f(u)\) in a bounded smooth domain with zero Dirichlet boundary condition. We use the method on harmonic extension to study the dependence of the number of sign-changing solutions on the parameter \(\lambda\).

MSC:

35J60 Nonlinear elliptic equations
35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
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