Two weak solutions for perturbed nonlocal fractional equations

In the present paper, we consider problems modeled by the following non-local fractional equation:where is fixed, is the fractional Laplace operator, are real parameters, is an open bounded subset of () with Lipschitz boundary , and are two suitable Caratheodory functions. By using variational methods, we prove the existence of at least two weak solutions for such problems for certain values of the parameters.