Critical Points Theorems via the Generalized Ekeland Variational Principle and its Application to Equations of p(x)-Laplace Type in RN

In this paper, we investigate abstract critical point theorems for continuously Gateaux differentiable functionals satisfying the Cerami condition via the generalized Ekeland variational principle developed by C.-K. Zhong. As applications of our results, under certain assumptions, we show the existence of at least one or two weak solutions for nonlinear elliptic equations with variable exponents - div(phi(x,del u)) + V(x)vertical bar u vertical bar(p (x)-2)u = lambda f (x,u) in R-N, where the function phi (x , v) is of type vertical bar v vertical bar(p(x) -2)v with a continuous function p:R-N -> (1, infinity), V: R-N -> (0, infinity) is a continuous potential function, lambda is a real parameter, and f : R-N X R -> R is a Caratheodory function. Especially, we localize precisely the intervals of lambda for which the above equation admits at least one or two nontrivial weak solutions by applying our critical points results.