mountain pass solutions to equation of p(x)-Laplacian type

it this work we consider the nonlinear boundary value problem with nonlinear boundary condition where is a bounded smooth domain of RN with smooth boundarey dev () is the so -called p(x laplacian operator and f and g are caratheodory functions by a direct variational approach and the theory of the variable exponent sobolev spaces under growth conditions on the reaction terms we establish the existence of positive solution.

mountain pass solutions to equation of p(x)-Laplacian type Keywords:

p(x -laplacian , growth conditions mountain pass lemma