On p(x)-Laplacian equations in RN with nonlinearity sublinear at zero

Let p, q be functions on RN satisfying 1≪q≪p≪N, we consider p(x)-Laplacian problems of the form (Formula presented.) To apply variational methods, we introduce a subspace X of W1,p(x)(RN) as our working space. Compact embedding from X into Lq(x)(RN) is established, this enable us to get nontrivial solution of the problem; and two sequences of solutions going to ∞ and 0 respectively, when g(x,·) is odd.