Abstract
In this paper, we examine the existence of multiple solutions of parametric fractional equations involving the square root of the Laplacian in a smooth bounded domain () and with Dirichlet zero-boundary conditions, i.e.
The existence of at least three -bounded weak solutions is established for certain values of the parameter requiring that the nonlinear term f is continuous and with a suitable growth. Our approach is based on variational arguments and a variant of Caffarelli–Silvestre’s extension method.
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Notes
No potential conflict of interest was reported by the authors.