Research
Existence and multiplicity of solutions for nonlocal p
(
x
)
R
N
School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P.R. China
Boundary Value Problems 2012, 2012:79 doi:10.1186/1687-2770-2012-79
Published: 26 July 2012Abstract
In this paper, we study the nonlocal 
-Laplacian problem of the following form
By using the method of weight function and the theory of the variable exponent Sobolev space, under appropriate assumptions on f and M, we obtain some results on the existence and multiplicity of solutions of this problem. Moreover, we get much better results with f in a special form.
MSC: 35B38, 35D05, 35J20.
Keywords:
critical points;-Laplacian; nonlocal problem; variable exponent Sobolev spaces
