zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Solvability of a quadratic Hammerstein integral equation in the class of functions having limits at infinity. (English) Zbl 1223.45006
The authors prove that a quadratic Hammerstein integral equation has solutions in the class of real functions defined, bounded, continuous on the real half-axis and having limits at infinity. The main tool used in this investigation is the technique of measures of noncompactness and the Darbo fixed point theorem. At last, an example is performed.

45G10Nonsingular nonlinear integral equations
47H30Particular nonlinear operators
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H08Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
Full Text: DOI
[1] R.P. Agarwal, D. O’Regan and P.J.Y. Wong, Positive solutions of differential, difference and integral equation , Kluwer Academic Publishers, Dordrecht, 1999. · Zbl 1157.34301
[2] R.R. Akmerov, M.I. Kamenskii, A.S. Potapov, A.E. Rodkina and B.N. Sadovskii, Measures of noncompactness and condensing operators , Birkhäuser Verlag, Basel, 1992. · Zbl 0748.47045
[3] J. Appell and P.P. Zabrejko, Nonlinear superposition operators , Cambridge University Press, Cambridge, 1990. · Zbl 0701.47041
[4] J.M. Ayerbe Toledano, T. Dominguez Benavides and G. Lopez Acedo, Measures of noncompactness in metric fixed point theory , Birkhäuser, Basel, 1997. · Zbl 0885.47021
[5] J. Banaś, Measures of noncompactness in the space of continuous tempered functions , Demon. Math. 14 (1981), 127-133. · Zbl 0462.47035
[6] J. Banaś and K. Goebel, Measures of noncompactness in Banach spaces , Lect. Notes Pure Appl. Math. 60 (1980), Dekker, New York. · Zbl 0441.47056
[7] J. Banaś, D. O’Regan and R.P. Agarwal, Measures of noncompactness and asymptotic stablility of solutions of a quadratic Hammerstein integral equation , Rocky Mountain J. Math.,
[8] J. Banaś, D. O’Regan and K. Sadarangani, On solutions of a quadratic Hammerstein integral equation on an unbounded interval , Dynamic Syst. Appl. 18 (2009), 251-264. · Zbl 1181.45013
[9] J. Banaś, J. Rocha Martin and K. Sadarangani, On solutions of a quadratic integral equation of Hammerstein type , Math. Comput. Model. 43 (2006), 97-104. · Zbl 1098.45003 · doi:10.1016/j.mcm.2005.04.017
[10] C. Corduneanu, Integral equations and applications , Cambridge University Press, Cambridge, 1991. · Zbl 0714.45002
[11] G. Darbo, Punti uniti in transformazioni a codominio non compatto , Rend. Sem. Math. Univ. Padova 24 (1955), 84-92. · Zbl 0064.35704 · numdam:RSMUP_1955__24__84_0 · eudml:106925
[12] K. Deimling, Nonlinear functional analysis , Springer Verlag, Berlin, 1985. · Zbl 0559.47040
[13] G.M. Fichtenholz, Differential and integral calculus , II, PWN, Warsaw, 1980 (in Polish). · Zbl 0900.26002
[14] J. Mawhin, On an existence result of Leray for nonlinear integral equations , Fixed Point Theory 7 (2006), 297-304. · Zbl 1119.45001
[15] D. O’Regan and M. Meehan, Existence theory for nonlinear integral and integrodifferential equations , Kluwer Academic Publishers, Dordrecht, 1998. · Zbl 0905.45003
[16] R. Stańczy, Hammerstein equations with an integral over a noncompact domain , Ann. Polon. Math. 69 (1998), 49-60. · Zbl 0919.45004
[17] Z. Yang, Nontrivial solutions of nonlinear Hammerstein integral equations , Nonlin. Funct. Anal. Appl. 10 (2005), 331-342. · Zbl 1086.45001
[18] P.P. Zabrejko, A.I. Koshelev, M.A. Krasnoselśkii, S.G. Mikhlin, L.S. Rakovschik and J. Stetsenko, Integral equations , Nordhoff, Leyden, 1975. · Zbl 0293.45001