The Existence Of Solutions To Two Types Of Nonlinear Elliptic Equations

This paper mainly studies the quasilinear Schrodinger equations.Firstly,we consider the following qussilinear Schrodinger problem with general nonlinear terms and critical term:(?) where ?>0 is a constant,V:RN?R and g ? C(R,R).Supposing that g does not satisfy Ambrosetti-Rabinowitz((AR)for short)growth condition,by using the changes of variables and Pohozaev manifold,we proved that the limiting equation obtains the existence of positive ground state solution.Then combining a monotonicity trick and a global compactness lemma,we prove that this problem has a positive ground state solution.Secondly,we consider the following quasilinear Schrodinger problem with non-square diffusion:(?) where 1/2<?<1,V:RN?R is a potential function and g?C(RN ×R,R).By using a local linking argument and Morse theory,we prove that this problem has a nontrivial solution.