Infinitely many solutions for a p(x)p(x)-Laplacian equation in RNRN

This paper deals with a p(x)p(x)-Laplacian equation in RNRN. By means of a direct variational approach and the theory of the variable exponent Sobolev spaces, we establish the existence of infinitely many distinct homoclinic radially symmetric solutions whose W1,p(x)(RN)W1,p(x)(RN)-norms tend to zero (to infinity, respectively) under weaker hypotheses about nonlinearity at zero (at infinity, respectively).