Positive solution to the nonlinear abstract Hammerstein equation and applications to {\phi} -Laplacian BVPs |
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| Authors: | Abdelhamid Benmezaï Salima Mechrouk |
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| Institution: | 1. Dynamical Systems Laboratory, Faculty of Mathematics, USTHB, PO Box 32, El-Alia Bab-ezouar, Algiers, Algeria
2. Faculty of Sciences, University M’Hmed Bouguerra, Boumerdes, Algeria
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| Abstract: | We provide in this paper existence results for positive solution to the abstract Hammerstein equation NFu = u where N : E → E is a completely continuous operator, F : C → C is a continuous and bounded map and C is a cone in the Banach space E. The obtained results are used to prove existence results for positive solution to ${\phi}$ -Laplacian boundary value problem. |
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