The entire large solutions for a quasilinear Schrödinger elliptic equation by the dual approach - Zhang, Xinguang; Liu, Lishan; Wu, Yong Hong (Pergamon Press, 2016)
In this paper, we consider a Modified Nonlinear Schrödinger equation Δu−Δ(|u|2γ)|u|2γ−2u=q(x)F(u)Δu−Δ(|u|2γ)|u|2γ−2u=q(x)F(u) on View the MathML sourceRn(n≥3), where View the MathML sourceγ>12, qq is a nonnegative continuous function on View the MathML sourceRn, FF is a continuous positive and non-decreasing function on [0,∞)[0,∞). We establish sufficient conditions for the existence and nonexistence of positive entire large solutions for the given equation by using the dual approach.