Displaying similar documents to “Further higher monotonicity properties of Sturm-Liouville functions”

Singular solutions for the differential equation with p -Laplacian

Miroslav Bartušek (2005)

Archivum Mathematicum

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In the paper a sufficient condition for all solutions of the differential equation with p -Laplacian to be proper. Examples of super-half-linear and sub-half-linear equations ( | y ' | p - 1 y ' ) ' + r ( t ) | y | λ sgn y = 0 , r > 0 are given for which singular solutions exist (for any p > 0 , λ > 0 , p ≠ λ ).

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...

Generalised regular variation of arbitrary order

Edward Omey, Johan Segers (2010)

Banach Center Publications

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Let f be a measurable, real function defined in a neighbourhood of infinity. The function f is said to be of generalised regular variation if there exist functions h ≢ 0 and g > 0 such that f(xt) - f(t) = h(x)g(t) + o(g(t)) as t → ∞ for all x ∈ (0,∞). Zooming in on the remainder term o(g(t)) eventually leads to the relation f(xt) - f(t) = h₁(x)g₁(t) + ⋯ + hₙ(x)gₙ(t) + o(gₙ(t)), each g i being of smaller order than its predecessor g i - 1 . The function f is said to be generalised regularly...