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Paper   IPM / M / 16302
School of Mathematics
  Title:   Existence of solutions for a fractional equation in an unbounded domain
  Author(s):  Amin Esfahani
  Status:   Published
  Journal: J. Math. Phys.
  Year:  2020
  Pages:   DOI: 10.1063/1.5121762
  Supported by:  IPM
This paper focuses on the scalar field equation D^2α_x u−νu−u_yy=f(u), where α∈(0,1), (x,y)∈R^N×(−L,L)⊂R^N+1, with N≥1 and D^2α_ x stands for the fractional Laplacian. By using several variational methods, we establish the existence, long behavior, and multiplicity of solutions of this equation under the Dirichlet and Neumann boundary conditions.

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