Applications Of Critical Point Theory To Nonlinear Equations

In this thesis, the existence of infinitely many solutions for quasilinear elliptic equation on R^N, and multiple periodic solutions for nonlinear difference equations are obtained by variational methods. First, we use the Fountain theorem to obtain infinitely many solutions for quasilinear elliptic equationwhere△_pu = (?), 1 < p <∞. Here we consider the superlinear case: (?). Unlike the usual results, our f(x,u) does not satisfy the superlinear condition of Ambrosetti-Rabinowitz.Next, using the three critical points theorem and the clark theorem, we consider the existence of multiple periodic solutions for nonlinear difference equations of the formwhere m≥2 is a fixed integer,δ> 0,△is the forward difference operator defined by△x_n = x_n+1 - x_n, {p_n} is a nonnegative m-periodic real sequence; f is a continuous function on Z×R, which is m-periodic on the second variable. Throughout this thesis, the convention (-1)^δ= -1 is made.