Existence and multiplicity of sign-changing solitary waves for a quasilinear Schrödinger equation. Issue 13 (2nd September 2022) - Huang, Wentao; Wang, Li; Wang, Qingfang
ABSTRACT: This paper is motivated by the study of the following quasilinear Schrödinger equation 1 − Δ u + V ( x ) u − [ Δ ( 1 + u 2 ) 1 2 ] u 2 ( 1 + u 2 ) 1 2 = λ h ( u ), x ∈ R N, where N ≥ 3, λ > 0 is a parameter and V ( x ) is a given positive potential. As an example, the nonlinearity includes the pure power type of h ( u ) = | u | p − 2 u for the well-studied case 12 − 4 6 < p < 2 ∗, and the case 2 < p < 12 − 4 6 in which few existence results are known. Distinguishing from the existing results in the literature, we are more interested in the existence and multiplicity of sign-changing solutions for the above problem.