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 |
| Summary: | 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. |
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| ISSN: | 1072-6691 |