By Ondřej Doślý and Pavel Řehák (Eds.)

ISBN-10: 0444520392

ISBN-13: 9780444520395

The publication offers a scientific and compact therapy of the qualitative idea of half-lineardifferential equations. It comprises the main up to date and entire fabric and represents the 1st try to current the result of the swiftly constructing idea of half-linear differential equations in a unified shape. the most issues coated by way of the ebook are oscillation and asymptotic conception and the speculation of boundary worth difficulties linked to half-linear equations, however the e-book additionally features a remedy of comparable issues like PDE's with p-Laplacian, half-linear distinction equations and diverse extra basic nonlinear differential equations.- the 1st entire therapy of the qualitative thought of half-linear differential equations.- comparability of linear and half-linear theory.- Systematic method of half-linear oscillation and asymptotic theory.- accomplished bibliography and index.- precious as a reference ebook within the subject.

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**Additional resources for Half-Linear Differential Equations**

**Example text**

25) v2 - tp~lw{t) = KtF'{v2) ->Q as i ^ oo since F'(v2) < 0. 25) we have and using the formula (1 + a)p^1 = 1 + (p — l)a + o(a) as a —> 0, we obtain (with q = p/(p-l)) m = ^ ^ (i - ktF'^)q" ~ *^M (i - ktF'^), as t —> oo, here f ~ g for a pair of functions f,g means Hindoo "%y = 1, and K is a real constant. Thus x(t) = tX2exp{ktF'{v2)} ~iA2 as t -> oo, since F'{y2) < 0, where K is another real constant and A2 = &~1(v2) is the larger of the roots of the equation G(X) = 0. 40 Chapter 1. Basic Theory Case Ic) v(S) > v2.

2. 1), which can be the same as in the linear case. 2. 1) is disconjugate on [To,Ti] for every T\ > To. 1) is said to be oscillatory. 1) is oscillatory. 1) means the existence of a sequence of zeros of this solution tending to oo. 1). 1) cannot a have a finite cluster point. 1). The next statement is an extension of well-known Sturm comparison theorem 18 Chapter 1. 1). 4. \. 6) has a zero in (£i, £2) or it is a multiple of the solution x. 7) is strict on a set of positive measure. Proof. 1) having zeros at t = t\ and £ = £2.

17) and correspond to x and y, respectively. 20) satisfying the initial conditions

### Half-Linear Differential Equations by Ondřej Doślý and Pavel Řehák (Eds.)

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