Stationary waves of Schr\"{o}dinger-type equations with variable   exponent
  We are concerned with a class of nonlinear Schr\"{o}dinger-type equations with a reaction term and a differential operator that involves a variable exponent. By using related variational methods, we establish several existence results. 
Du\v{s}an D. Repov\v{s}
math.AP math.FA