Ling Ding, Yi-Jie Meng, Shi-Wu Xiao, Jin-Ling Zhang
Abstract:
In this article we study the Kirchhoff type equation
involving a linear part
which is coercive
if
and is noncoercive if
,
a nonlocal nonlinear term
and a sign-changing nonlinearity of the form
, where
,
is a real parameter and
is the first eigenvalue
of
. Under suitable assumptions on
f and h, we obtain positives solution for
and two positive solutions with a condition on k.
Submitted August 20, 2015. Published January 25, 2016.
Math Subject Classifications: 35J60, 35B38, 35A15.
Key Words: Indefinite Kirchhoff equation; concentration compactness lemma;
(PS) condition; Ekeland's variational principle.
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Ling Ding School of Mathematics and Computer Science Hubei University of Arts and Science Hubei 441053, China email: dingling1975@qq.com, dingling19750118@163.com | |
Yi-Jie Meng School of Mathematics and Computer Science Hubei University of Arts and Science Hubei 441053, China email: 245330581@qq.com | |
Shi-Wu Xiao School of Mathematics and Computer Science Hubei University of Arts and Science Hubei 441053, China email: xshiwu@sina.com | |
Jin-Ling Zhang School of Mathematics and Computer Science Hubei University of Arts and Science Hubei 441053, China email: jinling48@163.com |
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