L-P-solutions of singular integro-differential equations
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Burton, T. A.
Purnaras, I. K.
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Elsevier
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peer reviewed
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Journal of Mathematical Analysis and Applications
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We study a variety of scalar integro-differential equations with singular kernels including linear, nonlinear, and resolvent equations. The first result involves a type of existence theorem which uses a fixed point mapping defined by the integro-differential equation itself and produces a unique solution with a continuous derivative in a very simple way. We then construct a Liapunov functional yielding qualitative properties of solutions. The work answers questions raised by Volterra in 1928, by Levin in 1963, and by Grimmer and Seifert in 1975. Previous results had produced bounded solutions from bounded perturbations. Our results mainly concern integrable solutions from integrable perturbations. (C) 2011 Elsevier Inc. All rights reserved.
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integro-differential equations, liapunov functionals, singular kernels, l-p solutions
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<Go to ISI>://000295563500029
http://ac.els-cdn.com/S0022247X11007888/1-s2.0-S0022247X11007888-main.pdf?_tid=8cf47932-cf38-11e2-9104-00000aab0f02&acdnat=1370585436_9f63bb49ebcd62608659782cb4fe8521
http://ac.els-cdn.com/S0022247X11007888/1-s2.0-S0022247X11007888-main.pdf?_tid=8cf47932-cf38-11e2-9104-00000aab0f02&acdnat=1370585436_9f63bb49ebcd62608659782cb4fe8521
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en
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Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών