Existence And Multiplicity Of Solutions For P-Laplacian And P(x)-Laplacian Equations

The contents of this paper are as follows:Firstly, we study the following semilinear elliptic equation with Dirichlet boundaryvalue problem:in the subcritical growth case we obtain at least two nontrival solutions by using the three-critical-point theorem and the reduction method.Secondly, we discuss the following quasilinear elliptic equation with Dirichlet boundary value problem(p > 1):when the Ambrosetti-Rabinowitz condition (AR) cannot be supposed, using the improved mountain pass lemmas, we get a positive solution and multiple solutions under an asymptotically linear condition.Finally, we study the following p(x)-Laplacian equation(p(x) > 1):by using a " Fountain Theorem ", we get infinity many solutions under an superlinear condition.