On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation - Li, Guofa; Qiu, Chong; Cheng, Bitao; Wang, Wenbo (Frontiers in Physics, 2023)
In this paper, we consider the nonexistence and existence of solutions for a generalized quasilinear Schrödinger equation with a Kirchhoff-type perturbation. When the nonlinearity h(u) is critical or supercritical growth at infnity, the nonexistence result for quasilinear Schrödinger equation is proved via Pohožaev identity. If h(u) is asymptotically cubic growth at infinity, the existence of positive radial solutions for quasilinear Schrödinger equation are obtained for b is large or equal to 0 and b is equal to 0 by the variational methods. Moreover, some properties are established as the parameter b tends to 0.