Some existence and nonexistence theorems for solutions of degenerate parabolic equations : H. A. Levine and P. E. Sacks, Depatment of Mathematics, Iowa State University, Ames, Iowa 50011, USA

Abstract

In this paper, we consider a Modified Nonlinear Schrödinger equation Δu−Δ(|u|2γ)|u|2γ−2u=q(x)F(u) on Rn(n≥3), where γ>12, q is a nonnegative continuous function on Rn, F is a continuous positive and non-decreasing function on [0,∞). We establish sufficient conditions for the existence and nonexistence of positive entire large solutions for the given equation by using the dual approach.