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Displaying similar documents to “Singular solutions for the differential equation with p -Laplacian”

Further higher monotonicity properties of Sturm-Liouville functions

Zuzana Došlá, Miloš Háčik, Martin E. Muldoon (1993)

Archivum Mathematicum

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Suppose that the function q ( t ) in the differential equation (1) y ' ' + q ( t ) y = 0 is decreasing on ( b , ∞ ) where b ≥ 0 . We give conditions on q which ensure that (1) has a pair of solutions y 1 ( t ) , y 2 ( t ) such that the n -th derivative ( n ≥ 1 ) of the function p ( t ) = y 1 2 ( t ) + y 2 2 ( t ) has the sign ( - 1 ) n + 1 for sufficiently large t and that the higher differences of a sequence related to the zeros of solutions of (1) are ultimately regular in sign.

On the differentiability of certain saltus functions

Gerald Kuba (2011)

Colloquium Mathematicae

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We investigate several natural questions on the differentiability of certain strictly increasing singular functions. Furthermore, motivated by the observation that for each famous singular function f investigated in the past, f’(ξ) = 0 if f’(ξ) exists and is finite, we show how, for example, an increasing real function g can be constructed so that g ' ( x ) = 2 x for all rational numbers x and g’(x) = 0 for almost all irrational numbers x.

Remarks on the uniqueness of second order ODEs

Dalibor Pražák (2011)

Applications of Mathematics

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We are concerned with the uniqueness problem for solutions to the second order ODE of the form x ' ' + f ( x , t ) = 0 , subject to appropriate initial conditions, under the sole assumption that f is non-decreasing with respect to x , for each t fixed. We show that there is non-uniqueness in general; on the other hand, several types of reasonable additional assumptions make the problem uniquely solvable. The interest in this problem comes, among other, from the study of oscillations of lumped parameter systems...