Author:
Li Jiameng,Chen Huiwen,He Zhimin,Ouyang Zigen
Abstract
AbstractIn this article, we study the quasilinear Schrödinger equation $$ -\triangle (u)+V(x)u-\triangle \bigl(u^{2}\bigr)u=g(x,u), \quad x\in \mathbb{R}^{N}, $$
−
△
(
u
)
+
V
(
x
)
u
−
△
(
u
2
)
u
=
g
(
x
,
u
)
,
x
∈
R
N
,
where the potential $V(x)$
V
(
x
)
and the primitive of $g(x,u)$
g
(
x
,
u
)
are allowed to be sign-changing. Under more general superlinear conditions on g, we obtain the existence of infinitely many nontrivial solutions by using the mountain pass theorem. Recent results in the literature are significantly improved.
Funder
National Natural Science Foundation of China
Scientific Foundation of Hunan Provincial Education Department
Hunan Provin- cial Natural Science Foundation of China
Doctor Priming Fund Project of University of South China
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis