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Monotonic solutions for quadratic integral equations

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EN
Abstrakty
EN
Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.
Twórcy
  • Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
  • Department of Mathematics, Faculty of Sciences, Alexandria University at Damanhour, 22511 Damanhour, Egypt
Bibliografia
  • [1] G. Anichini and G. Conti, Existence of solutions of some quadratic integral equations, Opuscula Mathematica 28 (2008), 433-440. doi: 10.7151/dmdico.1132
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  • [6] J. Banaś and A. Chlebowicz, On integrable solutions of a nonlinear Volterra integral equation under Carathéodory conditions, Bull. London Math. Soc. 41 (2009), 1073-1084.
  • [7] J. Banaś and W.G. El-Sayed, Measures of noncompactness and solvability of an integral equation in the class of functions of locally bounded variation, J. Math. Anal. Appl. 167 (1992), 133-151. doi: 10.1016/0022-247X(92)90241-5
  • [8] J. Banaś and W.G. El-Sayed, Solvability of Functional and Integral Equations in some Classes of Integrable Functions, Politechnika Rzeszowska, Rzeszów, 1993.
  • [9] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Lect. Notes in Math. 60, M. Dekker, New York-Basel, 1980.
  • [10] J. Banaś, J. Rocha and K.B. Sadarangani, Solvability of a nonlinear integral equation of Volterra type, J. Comp. Appl. Math. 157 (2003), 31-48. doi: 10.1016/S0377-0427(03)00373-X
  • [11] J. Banaś and B. Rzepka, On existence and asymptotic stability of a nonlinear integral equation, J. Math. Anal. Appl. 284 (2003), 165-173. empty
  • [12] J. Banaś and B. Rzepka, Monotonic solutions of a quadratic integral equation of fractional order, J. Math. Anal. Appl. 332 (2007), 1371-1379. doi: 10.1016/j.jmaa.2006.11.008
  • [13] J. Banaś and B. Rzepka, Nondecreasing solutions of a quadratic singular Volterra integral equation, Math. Comp. Model. 49 (2009), 488-496. doi: 10.1016/j.mcm.2007.10.021
  • [14] J. Banaś, M. Lecko and W.G. El-Sayed, Existence theorems of some quadratic integral equations, J. Math. Anal. Appl. 222 (1998), 276-285. doi: 10.1006/jmaa.1998.5941
  • [15] J. Banaś and T. Zając, Solvability of a functional integral equation of fractional order in the class of functions having limits at infinity, Nonlin. Anal. Th. Meth. Appl. 71 (2009), 5491-5500. doi: 10.1016/j.na.2009.04.037
  • [16] J. Banaś and L. Olszowy, Measures of noncompactness related to monotonicity, Comment. Math. 41 (2001), 13-23.
  • [17] J. Caballero, A.B. Mingarelli and K. Sadarangani, Existence of solutions of an integral equation of Chandrasekhar type in the theory of radiative transfer, Electr. J. Differ. Equat. 57 (2006), 1-11.
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  • [20] M.A. Darwish, On solvability of some quadratic functional-integral equation in Banach algebra, Commun. Appl. Anal. 11 (2007), 441-450.
  • [21] M.A. Darwish and J. Henderson, Existence and asymptotic stability of solutions of a perturbed quadratic fractional integral equations, Fract. Calculus Appl. Anal. 12 (2009), 71-86.
  • [22] M.A. Darwish and S.K. Ntouyas, Monotonic solutions of a perturbed quadratic fractional integral equation, Nonlin. Anal. Th. Meth. Appl. 71 (2009), 5513-5521. doi: 10.1016/j.na.2009.04.041
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  • [24] W.G. El-Sayed and B. Rzepka, Nondecreasing solutions of a quadratic integral equation of Urysohn type, Comp. Math. Appl. 51 (2006), 1065-1074. doi: 10.1016/j.camwa.2005.08.033
  • [25] S. Hu, M. Khavani and W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Analysis 34 (1989), 261-266. doi: 10.1080/00036818908839899
  • [26] M.A. Krasnosel'skii, P.P. Zabrejko, J.I. Pustyl'nik and P.E. Sobolevskii, Integral Operators in Spaces of Summable Functions, Noordhoff, Leyden, 1976.
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  • [28] M. Väth, Continuity of single- and multivalued superposition operators in generalized ideal spaces of measurable functions, Nonlin. Funct. Anal. Appl. 11 (2006), 607-646.
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Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1132
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