Multiplicity Of Solutions For Two Classes Of Quasilinear Elliptic Equations

In this paper, we consider two classes of quasilinear elliptic equations.First, we consider this equation:We assume that f(x, u) is (p—1)-superlinear at zero, sublinear at infinite and has a sign condition. Through the utilization of convex property and the condition of f, we derive the (PS) condition. And a global minimizer is natural achieved with the realization that the functional is coercive. Another nontrivial solution is found by the employment of Morse inequality. Finally we get two nontrivial solutions of the equation.Another equation is the following:Infinitely many radial solutions are found via the Principle of Symmetric Crit-icality and fountain theorem, when f(|x|,s) has subcritical growth,(AR) condition and is odd to s.