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Unbounded solutions of BVP for second order ODE with p -Laplacian on the half line

Yuji Liu, Patricia J. Y. Wong (2013)

Applications of Mathematics

By applying the Leggett-Williams fixed point theorem in a suitably constructed cone, we obtain the existence of at least three unbounded positive solutions for a boundary value problem on the half line. Our result improves and complements some of the work in the literature.

Zeros of derivatives of solutions to singular ( p , n - p ) conjugate BVPs

Irena Rachůnková, Staněk, Svatoslav (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Positive solutions of the singular ( p , n - p ) conjugate BVP are studied. The set of all zeros of their derivatives up to order n - 1 is described. By means of this, estimates from below of the solutions and the absolute values of their derivatives up to order n - 1 on the considered interval are reached. Such estimates are necessary for the application of the general existence principle to the BVP under consideration.

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