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Upper and lower solutions satisfying the inverse inequality

Irena Rachůnková (1997)

Annales Polonici Mathematici

We consider multipoint and two-point BVPs for second order ordinary differential equations with a Carathéodory right hand side. We prove the existence of solutions provided there exist upper and lower solutions of the BVP and the upper solution is less than the lower one.

φ -Laplacian BVPs with linear bounded operator conditions

Kamal Bachouche, Smaïl Djebali, Toufik Moussaoui (2012)

Archivum Mathematicum

The aim of this paper is to present new existence results for φ -Laplacian boundary value problems with linear bounded operator conditions. Existence theorems are obtained using the Schauder and the Krasnosel’skii fixed point theorems. Some examples illustrate the results obtained and applications to multi-point boundary value problems are provided.

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