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Description
Oscillations in Nonlinear SystemsBy focusing on ordinary differential equations that contain a small parameter, this concise graduate level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds. Part I of the text features
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Part II offers extensive treatment of periodic solutions, including the general theory for periodic solutions based on the work of Cesari-Halel-Gambill, with specific examples and applications of the theory. Part III covers various aspects of almost periodic solutions, including methods of averaging and the existence of integral manifolds. An indispensable resource for engineers and mathematicians with knowledge of elementary differential equations and matrices, this text is illuminated by numerous clear examples.
Binding Type: Paperback
Publisher: Dover Publications
Published: 05/20/2015
ISBN: 9780486673622
Pages: 192
Weight: 0.47lbs
Size: 8.42h x 5.37w x 0.40d
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Product Reviews
★★★★★ 5
great ball!
Size: Medium (2.5"), Style: Fetch Pack 2
My pitbull LOVES these. She is a power chewer and tough on balls and toys and tends to go through them insanely quick. She is still on her first ball out of this pack and its been at least two months. It is a little small for her mouth but she doesn’t seem to mind, as it has quickly become one of her favorites. Not a loud ball and it doesn’t usually make that wet chewy noise when shes going to town on it which is huge for me😂😂 Safe for my pittie so i’d imagine a smaller dog would be just fine.
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Reviewed in the United States on April 21, 2026
★★★★★ 5
Border Collie Approved: Easy to Clean, Durable, and Great Bounce
Size: Medium (2.5"), Style: Fetch Pack 2
These are the best balls out there for dogs. These fit great in the chuck-it ball launcher, which we need to wear out my border collie. They fit her mouth properly and, most importantly, do not absorb all the spit or water after a good rain. They are quick to clean off and have good weight so you can let them fly! Furthermore, they bounce well, which is perfect for my dog that likes to catch them on a bounce. The ball is a strong rubber, so should not be easy to chew up. I've used these for years, and the only time I've had to replace them is when one gets lost in the hay field. I highly suggest these as replacements for the common tennis balls.
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Reviewed in the United States on July 19, 2025
★★★★★ 4
Heavy duty.
Size: Medium (2.5"), Style: Fetch Pack 2
My dog was not interested, but it’s a good product
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Reviewed in the United States on April 11, 2026
★★★★★ 5
Treats and plenty of ball throwing with these doggie toy
Size: Medium (2.5"), Style: Fetch Pack 1
I have actually purchased these twice already. I love the one that glows in the dark but it still got lost in my yard lol. My dog is a big breed half pitt/Labrador so she did chew through one of them already. I play ball with her every single day but I DO have to take them away from her because she will destroy them. They are great to add in treats as well, that was one of the my favorite things about them as well. They do last just if you have an over zealous chewer do not let them keep them for long periods of time. They are a good value for the price. Buy them your dog will love it!
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Reviewed in the United States on August 2, 2025
★★★★★ 5
My Female GSD loves
Size: Medium (2.5"), Style: Fetch Pack 1, Size: Medium (2.5"), Style: Fetch Pack 1
Shasta is my smallest. Six in December (2025) along with her brother. She’s 100 lbs and outside, completely ball driven see last picture. Don’t let the size (2.5”) of these Chuck-It balls deter you. If your larger Breed dog has any orthopedic issues, has already torn their ACL etc, one has arthritis but wants to play. This size is perfect!
Shazzy was born with several ortho issues. I don’t throw balls distance but right to her. This size and lighter weight assure even when Shazzy is spazzy w excitement, she’ll catch the ball mid air.
The green balls are softer, and glow in the dark. In summer we can play well past dusk and I can see them!
Her personality shows in the pictures. Playing ball is part of her. These balls are just perfect for her situation. Somehow they disappear, she loves making baskets, puts them in my tractor bucket, or my gardening bucket..then get put in burn pile, trash etc. I keep replacing them because she’d look day and night if we actually ran out!! 🙏✝️👍🏼👍🏼
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Reviewed in the United States on September 3, 2025