An affine Birkhoff--Kellogg type result in cones with applications to functional differential equations

Abstract

In this short note we prove, by means of classical fixed point index, an affine version of a Birkhoff--Kellogg type theorem in cones. We apply our result to discuss the solvability of a class of boundary value problems for functional differential equations subject to functional boundary conditions. We illustrate our theoretical results in an example.

arXiv comment11 pages

References in corpus (4)

• Eigenvalues of elliptic functional differential systems via a Birkhoff--Kellogg type theorem
• Nontrivial solutions of boundary value problems for second order functional differential equations
• Existence of Positive Solutions for a Nonlinear Third-order Integral Boundary Value Problem
• On the solvability of a parameter-dependent cantilever-type BVP

Cited by in corpus (3)

• On fourth order retarded equations with functional boundary conditions: a unified approach
• A Birkhoff-Kellogg type theorem for discontinuous operators with applications
• On the solvability of parameter-dependent elliptic functional BVPs on annular-like domains