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Functions uniformly quiet at zero and existence results for one-parameter boundary value problems

G. L. Karakostas, P. Ch. Tsamatos (2002)

Annales Polonici Mathematici

We introduce the notion of uniform quietness at zero for a real-valued function and we study one-parameter nonlocal boundary value problems for second order differential equations involving such functions. By using the Krasnosel'skiĭ fixed point theorem in a cone, we give values of the parameter for which the problems have at least two positive solutions.

Further results for some third order differential systems with nonlinear dissipation

Awar Simon Ukpera (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We formulate nonuniform nonresonance criteria for certain third order differential systems of the form X ' ' ' + A X ' ' + G ( t , X ' ) + C X = P ( t ) , which further improves upon our recent results in [12], given under sharp nonresonance considerations. The work also provides extensions and generalisations to the results of Ezeilo and Omari [5], and Minhós [9] from the scalar to the vector situations.

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