Existence of positive solutions for a nonlinear quadratic integral equation
In this article, we study the existence of positive solutions for the nonlinear quadratic integral equation $$ x(t)=g(t,x(t))\int_{-\infty}^{t}a(t,t-s)f(s,x(s))ds,\quad t\in\mathbb{R}. $$ By using fixed point theory on cones, we prove the existence and uniqueness of bounded and continuous solu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2019-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/79/abstr.html |
| Summary: | In this article, we study the existence of positive solutions for the
nonlinear quadratic integral equation
$$
x(t)=g(t,x(t))\int_{-\infty}^{t}a(t,t-s)f(s,x(s))ds,\quad t\in\mathbb{R}.
$$
By using fixed point theory on cones, we prove the existence and uniqueness
of bounded and continuous solution with positive infimum. An example
illustrates the abstract result. |
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| ISSN: | 1072-6691 |