GENERAL EXISTENCE FOR MINIMUM PROBLEMS IN BANACH SPACES

In this note we give some extensions of a recent result concerning the minimum problems in Banach spaces. These extensions are based on the fact that the topological degree of a coercive map is one and this still remains true for a pseudomonotone potential map between a reflexive Banach space and its dual space. Some considerations concerning the minimum problem and the solution property of degree required in applications are also appended.