Displaying similar documents to “Properties of some integrals related to partial differential equations of order higher than two”

Integrals of Frullani type and the method of brackets

Sergio Bravo, Ivan Gonzalez, Karen Kohl, Victor H. Moll (2017)

Open Mathematics

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The method of brackets is a collection of heuristic rules, some of which have being made rigorous, that provide a flexible, direct method for the evaluation of definite integrals. The present work uses this method to establish classical formulas due to Frullani which provide values of a specific family of integrals. Some generalizations are established.

Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

P. Ch. Tsamatos (2004)

Annales Polonici Mathematici

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We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.