Existence and multiplicity of sign-changing solutions for a Schrödinger-Bopp-Podolsky system - Wang, Lixiong; Chen, Haibo; Liu, Senli (Topological Methods in Nonlinear Analysis, 2022)
In this paper, we deal with the following Schrödinger-Bopp-Podolsky system: equationP1 cases -Δ u+u+φ u=f(u), -Δφ +ε^2Δ^2φ =4π u^2, cases P_ε in R^3, equation where ε> 0 and f is a continuous, superlinear and subcritical nonlinearity. By using a perturbation approach and the method of invariant sets of descending flow incorporated with minimax arguments, we prove the existence and multiplicity of sign-changing solutions of syste (P1). Moreover, the asymptotic behavior of sign-changing solutions is also established. Our results mainly extend the results in Liu, Wang and Zhang ([Liuzhaoli2016AMPA], Ann. Mat. Pura Appl. 2016).