Download PDF by Vojislav Maric: Regular Variation and Differential Equations

By Vojislav Maric

ISBN-10: 3540465200

ISBN-13: 9783540465201

ISBN-10: 3540671609

ISBN-13: 9783540671602

This can be the 1st ebook providing an software of normal version to the qualitative thought of differential equations. The thought of standard version, brought by means of Karamata (1930), prolonged by means of numerous scientists, most importantly de Haan (1970), is a strong device in learning asymptotics in a number of branches of research and in likelihood thought. right here, a few asymptotic homes (including non-oscillation) of recommendations of moment order linear and of a few non-linear equations are proved by way of a brand new strategy that the well-developed idea of normal version has yielded. a very good graduate direction either in genuine research and in differential equations suffices for realizing the book.

Content point » Research

Keywords » Boundary layer equation - Differential equations of Thomas-Fermi kind - moment order linear differential equations

Related matters » Dynamical platforms & Differential Equations

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Additional resources for Regular Variation and Differential Equations

Sample text

2 are rapidly varying. g. a decreasing solution Ai(x) and x —+ oo, gives Ai(x) is rapidly varying which is easily verified by the definition. 3. Consider the self adjoint equation (_x yJ— ,\' xlnx+2x+2 \x+1 / x(x+1)21n2x y=O. 84) is fulfilled with c1 = 0. 85) holds since for some k> 0, [00 x/ Jx lnt+2+2/t cit

2. that it is normalized and decreasing and that by the Representation theorem is of the form yi(x) = exp {_ where ij(t) is positive and tends to zero as x —÷ oo. It also satisfies the integral equation ij(x) = x Furthermore by f(t)dt — x Theorem Li. Condition (L45) is fulfilled. 3) holds, the asymptotic representation for yi(x) will follow. 45) holds and then continue as above. It is worthwhile mentioning that not only for the existence but also for the asymptotic representation of slowly varying solutions, condition (L45) is the sole one needed.

In this special case asymptotic representation of solutions remains the same as before. 2. that it is normalized and decreasing and that by the Representation theorem is of the form yi(x) = exp {_ where ij(t) is positive and tends to zero as x —÷ oo. It also satisfies the integral equation ij(x) = x Furthermore by f(t)dt — x Theorem Li. Condition (L45) is fulfilled. 3) holds, the asymptotic representation for yi(x) will follow. 45) holds and then continue as above. It is worthwhile mentioning that not only for the existence but also for the asymptotic representation of slowly varying solutions, condition (L45) is the sole one needed.

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Regular Variation and Differential Equations by Vojislav Maric


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