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Positive solutions to a nonlinear abel-type integral equation on the whole line

✍ Scribed by W. Mydlarczyk; W. Okrasiński

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
449 KB
Volume
41
Category
Article
ISSN
0898-1221

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✦ Synopsis

consider the existence of positive solutions to the nonlinear integral equation / 5 U(Z) = Jl: -sY'&(s)) ds, (x E R, a 2 1)s

where g is a continuous, nondecreasing function such that g(0) = 0. We show that the equation always has nontrivial solutions and we give a necessary and sufficient condition for the existence of solutions u such that U(Z) > 0 for all z > -oo. We also provide a condition which ensures that all the nontrivial solutions experience the blow-up behaviour.

📜 SIMILAR VOLUMES

The existence problem for a nonlinear Ab
The existence problem for a nonlinear Abel equation on the half-line
✍ W. Mydlarczyk 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 231 KB

We discuss a nonlinear Abel equation on the half-line (-∞, c), c > 0. The basic results provide criteria for the existence of nontrivial everywhere positive solutions. They are expressed in terms of the generalized Osgood condition.