We study a nonlinear Steklov problem involving weighted p (. ) -Laplacian-like operator. Using some variational methods, we obtain the existence and multiplicity of solutions for the following problem aligned \ array{cc div ( (1+| u| ^p (x) 1+| u| ^{2p (x) }) a (x) | u| ^p (x) -2 u) =b (x) | u| ^p (x) -2u, & in \\ (1+| u| ^p (x) 1+| u| ^{2p (x) }) a (x) | u| ^p (x) -2 u = f (x, u), & on, array. aligned under some suitable conditions.
İsmail Aydın (Wed,) studied this question.