Existence Results for the Critical Biharmonic Elliptic Equation Involving Singular Nonlinearities

The present work is concerned with a class of biharmonic elliptic equations involving critical and singular nonlinearities. Under the assumption that p(x) attains its global maximum at some point, we derive that the problem admits a mountain pass type solution via the Brezis-Lieb lemma. Meanwhile, if p(x) has k global maximum points, we establish the existence of k nontrivial solutions by virtue of variational methods and the Nehari manifold.