ON EXISTENCE OF INFINITELY MANY WEEK SOLUTIONS TO A FRACTIONAL KIRCHHOFF PROBLEM

Abstract

In this paper, we consider the following nonlocal problem:

,
where λ is a real parameter and Ω is an open bounded subset of R3 with Lipschitz
boundary ∂Ω, s ∈ (3/4, 1), and the term f is a continuous function satisfying some
suitable conditions. Using Fountain Theorem and variational method in fractional Sobolev
space, we prove that there exist infinitely many weak solutions with unbounded energy
to above problem.