Nonexistence of solutions for quasilinear Schrödinger equation in ℝ^N

ABSTRACT

In this paper, we study the nonexistence of solutions to the quasilinear Schrödinger equations: (1) $\begin{array}{r}-{\mathrm{\Delta }}_{p}u+V\left(x\right)|u{|}^{p-2}u-{\mathrm{\Delta }}_p\left(|u{|}^{2\alpha }\right)|u{|}^{2\alpha -2}u=g(x,u),x\in {\mathbb{R}}^N,\end{array}$(1) where p-Laplacian operator ${\mathrm{\Delta }}_{p}u=\mathrm{d}\mathrm{i}\mathrm{v}\left(|\mathrm{\nabla }u{|}^{p-2}\mathrm{\nabla }u\right),1<p<N$ and $\alpha >1/2$ is a parameter. Under suitable conditions on $g(x,u)$, the nonexistence of solutions to Equation (1) is investigated.

Keywords:

• Quasilinear Schrödinger equations
• Pohazaev-type identity
• nonexistence of solutions

MSC:

• 35J20
• 35J70
• 35J92

Acknowledgements

The authors would like to express their sincere gratitude to the reviewers for valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11461016], Advanced Talents Foundation of QAU [grant number 6631115047].