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Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions

Saïd Abbas, Eman Alaidarous, Wafaa Albarakati, Mouffak Benchohra (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we use the upper and lower solutions method combined with Schauder's fixed point theorem and a fixed point theorem for condensing multivalued maps due to Martelli to investigate the existence of solutions for some classes of partial Hadamard fractional integral equations and inclusions.

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.

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