Avery fixed point theorem applied to Hammerstein integral equations
We apply a recent Avery et al. fixed point theorem to the Hammerstein integral equation $$ x(t)=\int^{T_2}_{T_1}G(t,s)f(x(s))\,ds, \quad t\in[T_1,T_2]. $$ Under certain conditions on G, we show the existence of positive and positive symmetric solutions. Examples are given where G is a convolu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2019-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/99/abstr.html |
| _version_ | 1818850180204593152 |
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| author | Paul W. Eloe Jeffrey T. Neugebauer |
| author_facet | Paul W. Eloe Jeffrey T. Neugebauer |
| author_sort | Paul W. Eloe |
| collection | DOAJ |
| description | We apply a recent Avery et al. fixed point theorem to the Hammerstein
integral equation
$$
x(t)=\int^{T_2}_{T_1}G(t,s)f(x(s))\,ds, \quad t\in[T_1,T_2].
$$
Under certain conditions on G, we show the existence of positive
and positive symmetric solutions. Examples are given where G is a
convolution kernel and where G is a Green's function associated with
different boundary-value problem. |
| first_indexed | 2024-12-19T06:45:02Z |
| format | Article |
| id | doaj.art-29d87d3dbbc34778a6b02e87d5df77d3 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-19T06:45:02Z |
| publishDate | 2019-08-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-29d87d3dbbc34778a6b02e87d5df77d32022-12-21T20:31:55ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912019-08-01201999,120Avery fixed point theorem applied to Hammerstein integral equationsPaul W. Eloe0Jeffrey T. Neugebauer1 Univ. of Dayton, Dayton, OH, USA Eastern Kentucky Univ., Richmond, KY, USA We apply a recent Avery et al. fixed point theorem to the Hammerstein integral equation $$ x(t)=\int^{T_2}_{T_1}G(t,s)f(x(s))\,ds, \quad t\in[T_1,T_2]. $$ Under certain conditions on G, we show the existence of positive and positive symmetric solutions. Examples are given where G is a convolution kernel and where G is a Green's function associated with different boundary-value problem.http://ejde.math.txstate.edu/Volumes/2019/99/abstr.htmlHammerstein integral equationboundary-value problemfractional boundary-value problem |
| spellingShingle | Paul W. Eloe Jeffrey T. Neugebauer Avery fixed point theorem applied to Hammerstein integral equations Electronic Journal of Differential Equations Hammerstein integral equation boundary-value problem fractional boundary-value problem |
| title | Avery fixed point theorem applied to Hammerstein integral equations |
| title_full | Avery fixed point theorem applied to Hammerstein integral equations |
| title_fullStr | Avery fixed point theorem applied to Hammerstein integral equations |
| title_full_unstemmed | Avery fixed point theorem applied to Hammerstein integral equations |
| title_short | Avery fixed point theorem applied to Hammerstein integral equations |
| title_sort | avery fixed point theorem applied to hammerstein integral equations |
| topic | Hammerstein integral equation boundary-value problem fractional boundary-value problem |
| url | http://ejde.math.txstate.edu/Volumes/2019/99/abstr.html |
| work_keys_str_mv | AT paulweloe averyfixedpointtheoremappliedtohammersteinintegralequations AT jeffreytneugebauer averyfixedpointtheoremappliedtohammersteinintegralequations |