Geodesic
Equations with discontinuous nonlinear semimonotone operators
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 7-12.

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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.
Classification : 45G10, 45N05, 47H15, 47H30, 47J05, 47N20
Keywords: semimonotone operators; uniformly convex Banach spaces 
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Buong, Nguyen. Equations with discontinuous nonlinear semimonotone operators. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 7-12. http://geodesic.mathdoc.fr/item/CMUC_1999__40_1_a1/