Existence and multiplicity of solutions for nonlocal [InlineEquation not available: see fulltext.]-Laplacian problems in [InlineEquation not available: see fulltext.]

In this paper, we study the nonlocal [InlineEquation not available: see fulltext.]-Laplacian problem of the following form [Equation not available: see fulltext.] 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.