Multiple homoclinic solutions for a class of superquadratic fourth-order differential equations

Abstract EN

Applying a Symmetric Mountain Pass Theorem, we prove the existence of in nitely many homoclinic solutions for a class of fourth-order di erential equations u(4)(x) + !u00(x) + a(x)u(x) = f(x; u(x)); 8x 2 R where a 2 C(R;R) may be negative on a bounded interval and F(x; u) = R u 0 f(x; t)dt is superquadratic at in nity in the second variable but does not need to satisfy the well-known Ambrosetti-Rabinowitz superquadratic growth condition.