Electron. J. Differential Equations, Vol. 2018 (2018), No. 102, pp. 1-11.

Unbounded solutions for Schrodinger quasilinear elliptic problems with perturbation by a positive non-square diffusion term

Carlos Alberto Santos, Jiazheng Zhou

In this article, we present a version of Keller-Osserman condition for the Schr\"odinger quasilinear elliptic problem
 -\Delta u+\frac{k}{2}u\Delta u^2=a(x)g(u)\quad\text{in } \mathbb{R}^N,\cr
 u>0\quad  \text{in }\mathbb{R}^N,\quad
 \lim_{|x|\to \infty} u(x)= \infty\,,
where $a:\mathbb{R}^N \to [0,\infty)$ and $g:[0,\infty) \to [0,\infty)$ are suitable continuous functions, $N \geq 1$, and $k>0$ is a parameter. By combining a dual approach and this version of Keller-Osserman condition, we show the existence and multiplicity of solutions.

Submitted October 10, 2017. Published May 3, 2018.
Math Subject Classifications: 35J10, 35J62, 35B08, 35B09, 35B44.
Key Words: Schrodinger equations; blow up solutions; quasilinear problem; non-square diffusion; multiplicity of solutions.

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Carlos Alberto Santos
Universidade de Brasília
Departamento de Matemática
70910-900, Brasília - DF, Brazil
email: csantos@unb.br
Jiazheng Zhou
Universidade de Brasília
Departamento de Matemática, 70910-900, Brasília - DF, Brazil
email: jiazzheng@gmail.com

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