Existence and nonexistence results for generalized quasilinear Schrödinger equations of Kirchhoff type in ℝ3. Issue 14 (25th October 2020)

• Record Type: Journal Article
• Authors: Shen, Liejun
• Is Part Of: Applicable analysis. Volume 99:Issue 14(2020)
• Page Start: 2465
• Page End: 2488
• Publication Date: 2020-10-25
• Subjects: Nonexistence -- generalized quasilinear -- Kirchhoff type -- link argument -- Nehari–Pohoz˘aev manifold; 35A15 -- 35J60 -- 35J62; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1569225
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: This paper is concerned with the existence and nonexistence results for generalized quasilinear Kirchhoff-type equations in 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.