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

Ziheng Zhang, Jianlun Liu

• In this paper we consider the following Klein–Gordon equation coupled with Born– Infeld theory −u + [m2 − (ω + φ)2]u = |u|p−2u in R3, φ + β4φ = 4π(ω + φ)u2 in R3, 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.