Existence and Multiplicity of Sign-Changing Solutions for Klein–Gordon Equation Coupled with Born–Infeld Theory with Subcritical Exponent

In this paper we consider the following Klein–Gordon equation coupled with Born–Infeld theory - Δ u + [ m 2 - ( ω + ϕ ) 2 ] u = | u | p - 2 u in R 3 , Δ ϕ + β Δ 4 ϕ = 4 π ( ω + ϕ ) u 2 in R 3 , where 2 < p < 6 , ω > 0 , β > 0 and m is a real constant. Assuming that 0 < ω < p 2 - 1 | m | and 2 < p < 4 or 0 < ω < | m | and 4 ≤ p < 6 , we obtain the existence and multiplicity of sign-changing solutions via the method of invariant sets of descending flow.