Existence of Solutions of a Nonlinear Hammerstein Integral Equation

Abstract

In this article, we are concerned with existence results for a nonlinear Hammerstein integral equation in L ¹ spaces. Making use of the De Blasi measure of weak noncompactness, we establish variants of some Krasnosel'skii type theorem involving the weak topology of Banach spaces.

Keywords:

• Fixed point theorems
• Measure of weak noncompactness
• Nonlinear Hammerstein equations
• Weak topology
• Weakly sequentially continuous

Mathematics Subject Classification:

• 47H10
• 47H30