Existence and nonexistence results for generalized quasilinear Schrödinger equations of Kirchhoff type in ℝ³

ABSTRACT

This paper is concerned with the existence and nonexistence results for generalized quasilinear Kirchhoff-type equations in ${\mathbb{R}}^3$ which have appeared from plasma physics, as well as high-power ultrashort laser in matter. By using a change of variables, we obtain the existence of solutions via Link argument, where a nonexistence result for a minimizing problem is also established by the Nehari–Pohoz˘aev manifold.

KEYWORDS:

• Nonexistence
• generalized quasilinear
• Kirchhoff type
• link argument
• Nehari–Pohoz˘aev manifold

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35A15
• 35J60
• 35J62

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The author was supported by National Natural Science Foundation of China (NSFC) (Grant No. 11371158, 11771165), the program for Changjiang Scholars and Innovative Research Team in University (No. IRT13066) and the excellent doctoral dissertation cultivation from Central China Normal University (Grant No. 2018YBZZ068).