Surjectivity results for a class of nonlinear operators in reflexive banach spaces

Abstract

The operator equation Au+Lu+µFu = h is studied in a reflexive Banach space X. Here, µ > 0 is constant and h ↦ X^* is fixed. The operators L,F are compact and A is strongly monotone. Degree arguments are used to show the existence of solutions of this equation and extension of the results in [3], [4] are established.

Keywords:

• reflexive Banach space,
• strong rnonotonicity,
• degree