On The Existence Of Nontrivial Solutions For P-Laplacian Equations Without (AR) Condition In R~N

In this paper, we study the following quasilinear equation:where K is a positive constant, and the nonlinearity f satisfies which does not satisfy the (AR) condition:It is difficult to obtain the existence of (PS) sequence and the boundedness of any(PS) sequence without the (AR) condition. Using the monotone method in [7] pro-posed by Jeanjean, we can obtain the bounded (PS) sequence by introducing a class of perturbation functionals, and then get the existence of positive solution for the given problem.