Geodesic
Existence and nonexistence results for quasilinear Schrödinger equations with a general nonlinear term
Yan-Fang Xue1 ; Ying Lv2 ; Chun-Lei Tang2
1School of Mathematics and Statistics Southwest University 400715 Chongqing, China and School of Mathematics and Statistics Xinyang Normal University 464000 Henan, China
2School of Mathematics and Statistics Southwest University 400715 Chongqing, China
Annales Polonici Mathematici, Tome 120 (2017) no. 3, pp. 271-293
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We study the quasilinear Schrödinger equation $$ -\varDelta u+V(x)u-\varDelta (u^2)u=g(u), \hskip 1em\ x\in \mathbb {R}^N, $$ where $V(x)$ tends to zero as $|x|\rightarrow \infty $ and $g(u)$ satisfies the general hypotheses introduced by Berestycki and Lions. We employ the mountain pass theorem to obtain the existence of a positive ground state solution. Moreover, we prove a nonexistence result by using the Pohozaev manifold.
DOI : 10.4064/ap170502-2-12
Keywords: study quasilinear schr dinger equation vardelta u vardelta hskip mathbb where tends zero rightarrow infty satisfies general hypotheses introduced berestycki lions employ mountain pass theorem obtain existence positive ground state solution moreover prove nonexistence result using pohozaev manifold

Yan-Fang Xue  1   ; Ying Lv  2   ; Chun-Lei Tang  2

1 School of Mathematics and Statistics Southwest University 400715 Chongqing, China and School of Mathematics and Statistics Xinyang Normal University 464000 Henan, China
2 School of Mathematics and Statistics Southwest University 400715 Chongqing, China 
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     title = {Existence and nonexistence results for quasilinear {Schr\"odinger} equations with a general nonlinear term},
     journal = {Annales Polonici Mathematici},
     pages = {271--293},
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Yan-Fang Xue; Ying Lv; Chun-Lei Tang. Existence and nonexistence results for quasilinear Schrödinger equations with a general nonlinear term. Annales Polonici Mathematici, Tome 120 (2017) no. 3, pp. 271-293. doi: 10.4064/ap170502-2-12

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