Periodic Solutions of a Class of Fourth-Order Superlinear Differential Equations

and Applied Analysis 3 Our main result is as follows. Theorem 2.3. Suppose a x , b x , and F satisfy A , F1 – F3 . Then System 1.2 has infinitely many distinct pairs of solutions zn un, vn , which are critical points of the functional I : X → R, and I zn → ∞ as n → ∞. In this paper, the existence of periodic solutions of a single equation in System 1.1 are extended to the case of equations, and also the cubic growth of nonlinear term is extended to a general form of superlinear growth. 3. Variational Structure and the Proof of Result In this section, we prove the main result stated in Section 2. 3.1. Variational Structure Denote X L ( H2 0, L ∩H1 0 0, L )2 . 3.1 Then X L is a Hilbert space. The norm is