Solutions Of Two Types Of Quasi-linear Elliptic Equations

This paper mainly studies quasilinear elliptic equation.The problem has a formal variational structure,but due to the quasilinear presence,it is difficult to find a suitable space in which the variational functional possesses both smoothness and compactness properties,we introduce two methods-dual approach and perturbation approach-to overcome the difficulties.Firstly,we consider the following quasilinear Schrodinger equation:(?).We focus on the case that the nonlinearity g(x,u)is sublinear growth in u.Under relaxed assumptions on V(x)which ensure the continuous embedding of working space,by using the method of dual approach,we prove that this equation has,infinitely many solutions with negative energy values and negative energy values converge to zero or a negative number.Recent results from the literature are extended.Secondly,we consider the following quasilinear Kirchhoff-Schrodinger-Poisson system:Due to the limitations of dual approach,we introduce perturbation approach to get in-finitely many sign-changing solutions with the integral constraint(?)nRN|u|pdx = 1,where A is a Lagrangian multiplier.