ABSTRACT
This chapter establishes a couple of constructive multiplicity results for A-proper Frechet differentiable mappings that are asymptotically close to linear A-proper mappings. It discusses the generality and a unifying feature of the theory. The chapter also discusses only briefly a couple of applications of some of the results to elliptic equations involving contractive type of nonlinearities in the highest order terms. It provides a couple of constructive multiplicity results for A-proper Frechet differentiable mappings which are asymptotically close to linear A-proper mappings. The chapter describes only a couple of results for elliptic equations involving perturbations of ball-condensing type. It shows that the sum of mappings of type (KS) and pseudo monotone or of type (KM) is of pseudo A-proper type.
