In this paper, we examine the existence of multiple solutions of parametric fractional equations involving the square root of the Laplacian A1/2 in a smooth bounded domain Ω ⊂ Rn (n ≥ 2) and with Dirichlet zero-boundary conditions, i.e. (Formula presented.) The existence of at least three L∞-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.
Multiple solutions of nonlinear equations involving the square root of the Laplacian
Vilasi L.
2017-01-01
Abstract
In this paper, we examine the existence of multiple solutions of parametric fractional equations involving the square root of the Laplacian A1/2 in a smooth bounded domain Ω ⊂ Rn (n ≥ 2) and with Dirichlet zero-boundary conditions, i.e. (Formula presented.) The existence of at least three L∞-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.File in questo prodotto:
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