Entire blow-up solutions for a quasilinear p-Laplacian Schrödinger equation with a non-square diffusion term

In this paper, we study the entire blow-up solutions for a quasilinear p-Laplacian Schrödinger elliptic equation with a non-square diffusion term. By using the dual approach and some new iterative techniques, the difficulty due to the non-square diffusion term and the p-Laplacian operator is overcome and the nonexistence and existence of entire blow-up solutions are established.