# Equations with discontinuous nonlinear semimonotone operators

Commentationes Mathematicae Universitatis Carolinae (1999)

- Volume: 40, Issue: 1, page 7-12
- ISSN: 0010-2628

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topBuong, Nguyen. "Equations with discontinuous nonlinear semimonotone operators." Commentationes Mathematicae Universitatis Carolinae 40.1 (1999): 7-12. <http://eudml.org/doc/248385>.

@article{Buong1999,

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.},

author = {Buong, Nguyen},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {semimonotone operators; uniformly convex Banach spaces; Hammerstein equation; nonlinear operator; semimonotone operator; discontinuous operator},

language = {eng},

number = {1},

pages = {7-12},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Equations with discontinuous nonlinear semimonotone operators},

url = {http://eudml.org/doc/248385},

volume = {40},

year = {1999},

}

TY - JOUR

AU - Buong, Nguyen

TI - Equations with discontinuous nonlinear semimonotone operators

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1999

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 40

IS - 1

SP - 7

EP - 12

AB - 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.

LA - eng

KW - semimonotone operators; uniformly convex Banach spaces; Hammerstein equation; nonlinear operator; semimonotone operator; discontinuous operator

UR - http://eudml.org/doc/248385

ER -

## References

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- Pavlenko V.N., Existence of solution for nonlinear equations involving discontinuous semimonotone operators (in Russian), Ukrainian Math. J. 33 (1981), 4 547-551. (1981)
- Raguimkhanov, Concerning an existence problem for solution of Hammerstein equation with discontinuous mappings (in Russian), Izvestia Vukov, Math. (1975), 10 62-70. (1975)
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