Abstract
In this paper, we study the existence of at least one positive solution to the fourth-order two-point boundary value problem (BVP)
which models a cantilever beam equation, where one end is kept free. Here \(f \in {\mathcal {C}}\left( [0,1] \times {\mathbb {R}}_{+}, {\mathbb {R}}_{+}\right) \), \(g \in {\mathcal {C}}\left( [0,1] , {\mathbb {R}}_{+}\right) \) and \(\lambda \) is a positive parameter. The sufficient conditions are interesting, new and easy to verify. We have used some inequalities on the nonlinear function f and eigenvalues of a linear integral operator as bounds for the parameter \(\lambda \) to obtain our results. Our approach is based on a revised version of a fixed point theorem due to Gustafson and Schmitt.
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Communicated by Sun-Sig Byun.
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Padhi, S. A Note on the Eigenvalue Criteria for Positive Solutions of a Cantilever Beam Equation with Free End. Bull. Iran. Math. Soc. 47, 1437–1451 (2021). https://doi.org/10.1007/s41980-020-00450-1
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DOI: https://doi.org/10.1007/s41980-020-00450-1