Existence of solutions for a class of quasilinear Schrödinger equation with a Kirchhoff-type.

In this paper, we discuss the existence of multiple solutions of the generalized quasilinear Schrödinger equation of Kirchhoff-type ... where b>0 is a parameter, g C¹(R,R⁺). In preceding approaches, the order of the nonlinear term f (x, t) about t at infinity is usually supposed to be higher than |t|³. But in this paper, this condition is not necessary. Under weaker condition ^t₀ f (x, s) ds = µ|G(t)|r - |G(t)|^r-1, where G(t) is the primitive function of g(t), 2 < r < 6, we get the existence of infinitely many solutions of the equation. Our work can be regarded as the extension of those such as [J. Zhang et al. Existence of multiple solutions of Kirchhoff type equation with sign-changing potential. Appl Math Comput. 2014;242:491-499] and related works. [ABSTRACT FROM AUTHOR]