Abstract:The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type $x+KF(x)=0$ with the discontinuous semimonotone operator $F$. Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in $L_p(\Omega )$ are given for illustration.
Keywords: semimonotone operators, uniformly convex Banach spaces
AMS Subject Classification: 47H15, 45G10, 45N05