Rectifiable oscillations in second-order half-linear differential equations (CROSBI ID 144966)
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Podaci o odgovornosti
Pašić, Mervan ; Wong, James S. W.
engleski
Rectifiable oscillations in second-order half-linear differential equations
Second-order half-linear differential equation (H): on the finite interval I = (0, 1] will be studied, where , p > 1 and the coefficient f(x) > 0 on I, , and . In case when p = 2, the equation (H) reduces to the harmonic oscillator equation (P): y′ ′ + f(x)y = 0. In this paper, we study the oscillations of solutions of (H) with special attention to some geometric and fractal properties of the graph . We establish integral criteria necessary and sufficient for oscillatory solutions with graphs having finite and infinite arclength. In case when , λ > 0, α > p, we also determine the fractal dimension of the graph G(y) of the solution y(x). Finally, we study the L p nonintegrability of the derivative of all solutions of the equation (H).
oscillations; nonlinear equations; graph; rectifiability; fractal dimension; Minkowski content; asymptotics; perturbation
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Podaci o izdanju
188 (3)
2009.
517-541
objavljeno
0373-3114
10.1007/s10231-008-0087-0