Fourth-order problems on W2,p()-extension domains involving Leray-Lions type operators

We establish the existence of infinitely many weak solutions for fourth-order problems without assuming the well-known Ambrosetti-Rabinowitz hypothesis and without imposing symmetry conditions. Instead, our nonlinear term only exhibits a suitable oscillatory behavior either at infinity or at zero. In fact, we work under very general hypotheses. Our class of domains includes both smooth and non-smooth domains. Our class of nonhomogeneous differential operators includes generalized Laplace operators, generalized mean curvature operators, generalized capillarity operators, p(),q()-biharmonic operators, as well as new nonstandard operators.