In this paper we study a highly nonlocal problem involving a fractional operator combined with a Kirchhoff-type coefficient. The latter is allowed to vanish at the origin (degenerate case). By working in a suitable fractional Sobolev space, which encode Dirichlet homogeneous boundary conditions, and exploiting the genus theory introduced by Krasnoselskii, we derive the existence of infinitely many weak solutions for this problem.
On a fractional Kirchhoff-type equation via Krasnoselskii's genus
MOLICA BISCI G;SERVADEI, RAFFAELLA
2015
Abstract
In this paper we study a highly nonlocal problem involving a fractional operator combined with a Kirchhoff-type coefficient. The latter is allowed to vanish at the origin (degenerate case). By working in a suitable fractional Sobolev space, which encode Dirichlet homogeneous boundary conditions, and exploiting the genus theory introduced by Krasnoselskii, we derive the existence of infinitely many weak solutions for this problem.File in questo prodotto:
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