Hammerstein–Nemytskii Type Nonlinear Integral Equations on Half-line in Space L 1 ( 0 , + ∞ ) ∩ L ∞ ( 0 , + ∞ )

Aghavard Kh. Khachatryan; Khachatur A. Khachatryan

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2013)

  • Volume: 52, Issue: 1, page 89-100
  • ISSN: 0231-9721

Abstract

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The paper studies a construction of nontrivial solution for a class of Hammerstein–Nemytskii type nonlinear integral equations on half-line with noncompact Hammerstein integral operator, which belongs to space L 1 ( 0 , + ∞ ) ∩ L ∞ ( 0 , + ∞ ) . This class of equations is the natural generalization of Wiener-Hopf type conservative integral equations. Examples are given to illustrate the results. For one type of considering equations continuity and uniqueness of the solution is established.

How to cite

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Khachatryan, Aghavard Kh., and Khachatryan, Khachatur A.. "Hammerstein–Nemytskii Type Nonlinear Integral Equations on Half-line in Space $L_1(0,+\infty )\cap L_{\infty }(0,+\infty )$." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.1 (2013): 89-100. <http://eudml.org/doc/260587>.

@article{Khachatryan2013,
abstract = {The paper studies a construction of nontrivial solution for a class of Hammerstein–Nemytskii type nonlinear integral equations on half-line with noncompact Hammerstein integral operator, which belongs to space $L_1(0,+\infty )\cap L_\{\infty \}(0,+\infty )$. This class of equations is the natural generalization of Wiener-Hopf type conservative integral equations. Examples are given to illustrate the results. For one type of considering equations continuity and uniqueness of the solution is established.},
author = {Khachatryan, Aghavard Kh., Khachatryan, Khachatur A.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Wiener–Hopf operator; Hammerstein–Nemytskii equation; Caratheodory condition; one-parameter family of positive solutions; iteration; monotonic increasing and bounded solution; Wiener-Hopf operator; Hammerstein-Nemytskii equation; nonlinear integral equations; noncompact integral operator},
language = {eng},
number = {1},
pages = {89-100},
publisher = {Palacký University Olomouc},
title = {Hammerstein–Nemytskii Type Nonlinear Integral Equations on Half-line in Space $L_1(0,+\infty )\cap L_\{\infty \}(0,+\infty )$},
url = {http://eudml.org/doc/260587},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Khachatryan, Aghavard Kh.
AU - Khachatryan, Khachatur A.
TI - Hammerstein–Nemytskii Type Nonlinear Integral Equations on Half-line in Space $L_1(0,+\infty )\cap L_{\infty }(0,+\infty )$
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 1
SP - 89
EP - 100
AB - The paper studies a construction of nontrivial solution for a class of Hammerstein–Nemytskii type nonlinear integral equations on half-line with noncompact Hammerstein integral operator, which belongs to space $L_1(0,+\infty )\cap L_{\infty }(0,+\infty )$. This class of equations is the natural generalization of Wiener-Hopf type conservative integral equations. Examples are given to illustrate the results. For one type of considering equations continuity and uniqueness of the solution is established.
LA - eng
KW - Wiener–Hopf operator; Hammerstein–Nemytskii equation; Caratheodory condition; one-parameter family of positive solutions; iteration; monotonic increasing and bounded solution; Wiener-Hopf operator; Hammerstein-Nemytskii equation; nonlinear integral equations; noncompact integral operator
UR - http://eudml.org/doc/260587
ER -

References

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  1. Arabadjyan, L. G., Yengibaryan, N. B., Convolution equations and nonlinear functional equations, Itogi nauki i teckniki, Math. Analysis 4 (1984), 175–242 (in Russian). (1984) MR0780564
  2. Gokhberg, I. Ts., Feldman, I. A., Convolution Equations and Proections Methods of Solutions, Nauka, Moscow, 1971. (1971) MR0355674
  3. Khachatryan, A. Kh., Khachatryan, Kh. A., 10.7494/OpMath.2011.31.3.393, Opuscula, Mathematica 31, 3 (2011), 393–398. (2011) Zbl1228.45007MR2802902DOI10.7494/OpMath.2011.31.3.393
  4. Khachatryan, A. Kh., Khachatryan, Kh. A., On solvability of a nonlinear problem in theory of income distribution, Eurasian Math. Jounal 2 (2011), 75–88. (2011) Zbl1258.45004MR2910832
  5. Khachatryan, Kh. A., On one class of nonlinear integral equations with noncompact operator, J. Contemporary Math. Analysis 46, 2 (2011), 71–86. (2011) MR2828824
  6. Khachatryan, Kh. A., Some classes of Urysohn nonlinear integral equations on half line, Docl. NAS Belarus 55, 1 (2011), 5–9. (2011) MR2932258
  7. Kolmogorov, A. N., Fomin, V. C., Elements of Functions Theory and Functional Analysis, Nauka, Moscow, 1981 (in Russian). (1981) 
  8. Lindley, D. V., The theory of queue with a single sever, Proc. Cambridge Phil. Soc. 48 (1952), 277–289. (1952) MR0046597
  9. Milojevic, P. S., A global description of solution to nonlinear perturbations of the Wiener–Hopf integral equations, El. Journal of Differential Equations 51 (2006), 1–14. (2006) MR2226924

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